Maths-
General
Easy

Question

Use the square of a binomial to find the value. 722

Hint:

The methods used to find the product of binomials are called special products.
Multiplying a number by itself is often called squaring.
For example (x + 3)(x + 3) = (x + 3)2

The correct answer is: 5184.


    722 can be written as  (70 + 2)2 which can be further written as (70 + 2)(70 + 2)
    (70 + 2)(70 + 2) = 70(70 + 2) + 2(70 + 2)

    =  70(70) +  70(2) + 2(70) + 2(2)

    = 4900 + 140 + 140 + 4

    = 4900 + 280 + 4

    = 5184
    Final Answer:
    Hence, the value of 722 is 5184.

    Related Questions to study

    General
    Maths-

    What is the gradient of a line parallel to the line whose equation -2x + y = -7 is:

    Hint:
    The slope/ gradient of a line is the measure of steepness of a line. It is understood that the slope of all parallel lines in the xy plane are equal. So first, we find the slope from the given equation of a line by using the slope intercept form of a line which is y = mx + c, , where m is slope and c is the y intercept. This gradient will be equal to the gradient of any line parallel to it.
    Step by step solution:
    The given equation of the line is
    -2x + y = -7
    We convert this equation in the slope intercept form, which is
    y = mx + c
    Where m is the slope of the line and c is the y-intercept.
    We rewrite the equation -2x + y - 7, as below
    y = 2x - 7
    Comparing with y = mx + c, we get that m = 2
    Thus, the gradient of line -2x + y = 7 is m = 2.
    We know that the gradient of any two parallel lines in the xy plane is always equal.
    Hence, the gradient of a line parallel to the line whose equation -2x + y = -7 is m = 2.
    Note:
    We can find the slope and y-intercept directly from the general form of the equation too; slope =negative a over b  and y-intercept = c over b, where the general form of equation of a line is ax + by + c = 0. Using this method, be careful to check that the equation is in general form before applying the formula. Here, we have, a = -2, b = 1, so we get m equals negative fraction numerator negative 2 over denominator 1 end fraction equals 2

    What is the gradient of a line parallel to the line whose equation -2x + y = -7 is:

    Maths-General
    Hint:
    The slope/ gradient of a line is the measure of steepness of a line. It is understood that the slope of all parallel lines in the xy plane are equal. So first, we find the slope from the given equation of a line by using the slope intercept form of a line which is y = mx + c, , where m is slope and c is the y intercept. This gradient will be equal to the gradient of any line parallel to it.
    Step by step solution:
    The given equation of the line is
    -2x + y = -7
    We convert this equation in the slope intercept form, which is
    y = mx + c
    Where m is the slope of the line and c is the y-intercept.
    We rewrite the equation -2x + y - 7, as below
    y = 2x - 7
    Comparing with y = mx + c, we get that m = 2
    Thus, the gradient of line -2x + y = 7 is m = 2.
    We know that the gradient of any two parallel lines in the xy plane is always equal.
    Hence, the gradient of a line parallel to the line whose equation -2x + y = -7 is m = 2.
    Note:
    We can find the slope and y-intercept directly from the general form of the equation too; slope =negative a over b  and y-intercept = c over b, where the general form of equation of a line is ax + by + c = 0. Using this method, be careful to check that the equation is in general form before applying the formula. Here, we have, a = -2, b = 1, so we get m equals negative fraction numerator negative 2 over denominator 1 end fraction equals 2
    General
    Maths-

    Two sides of a rectangle are (3p+5q) units and ( 5p-7q ) units. What is its area?

    Answer:
    • Hint:
    The concept used in the question is the area of a rectangle.
    The area of the rectangle is the product of sides.
    • Step by step explanation:
    ○     Given:
    Two sides of a rectangle
    (3p+5q) units and ( 5p-7q ) units.
    ○     Step 1:
    We know, the area of rectangle is product of its sides
    i.e. area = side × side
    So,
    Area = (3p+5q) × (5p-7q)
    = 3p (5p -7q) + 5q(5p-7q)
    = 15p2 - 21pq + 25pq - 35q2
    = 15p2 + 4pq - 35q2 sq. units
    • Final Answer:
    Hence, the area of the rectangle is 15p2 + 4pq - 35q2 sq. units.

    Two sides of a rectangle are (3p+5q) units and ( 5p-7q ) units. What is its area?

    Maths-General
    Answer:
    • Hint:
    The concept used in the question is the area of a rectangle.
    The area of the rectangle is the product of sides.
    • Step by step explanation:
    ○     Given:
    Two sides of a rectangle
    (3p+5q) units and ( 5p-7q ) units.
    ○     Step 1:
    We know, the area of rectangle is product of its sides
    i.e. area = side × side
    So,
    Area = (3p+5q) × (5p-7q)
    = 3p (5p -7q) + 5q(5p-7q)
    = 15p2 - 21pq + 25pq - 35q2
    = 15p2 + 4pq - 35q2 sq. units
    • Final Answer:
    Hence, the area of the rectangle is 15p2 + 4pq - 35q2 sq. units.
    General
    Maths-

    Find the error in the given statement.
    All monomials with the same degree are like terms.

    Explanation:
    • We have been given a statement in the question for which we have to find the error in the given statement.
    Step 1 of 1:
    We have given a statement all monomials with the same degree are like terms.
    The above statement is not true always.
    The variable should also be same.
    Example:4x, 5y
    Here both have degree one and both are monomials,
    But since, The variables are not same they are not like terms.

    Find the error in the given statement.
    All monomials with the same degree are like terms.

    Maths-General
    Explanation:
    • We have been given a statement in the question for which we have to find the error in the given statement.
    Step 1 of 1:
    We have given a statement all monomials with the same degree are like terms.
    The above statement is not true always.
    The variable should also be same.
    Example:4x, 5y
    Here both have degree one and both are monomials,
    But since, The variables are not same they are not like terms.
    parallel
    General
    Maths-

    Write equation of the line containing (-3, 4) and (-1, -2)

    Hint:
    We are given two points and we need to find the equation of the line passing through them. Recall that the equation of a line passing through two points (a, b) and (c, d) is given by
    Step by step solution:
    Let the given points be denoted by
    (a, b) = (-3, 4)
    (c, d) = (-1, -2)
    The equation of a line passing through two points (a, b) and (c, d) is
    fraction numerator y minus d over denominator d minus b end fraction equals fraction numerator x minus c over denominator c minus a end fraction
    Using the above points, we have
    fraction numerator y minus left parenthesis negative 2 right parenthesis over denominator negative 2 minus 4 end fraction equals fraction numerator x minus left parenthesis negative 1 right parenthesis over denominator negative 1 minus left parenthesis negative 3 right parenthesis end fraction
    Simplifying the above equation, we have
    fraction numerator y plus 2 over denominator negative 6 end fraction equals fraction numerator x plus 1 over denominator negative 1 plus 3 end fraction
    not stretchy rightwards double arrow fraction numerator y plus 2 over denominator negative 6 end fraction equals fraction numerator x plus 1 over denominator 2 end fraction
    Cross multiplying, we get
    2(y + 2) = -6(x + 1)
    Expanding the factors, we have
    2y + 4 = -6x - 6
    Taking all the terms in the left hand side, we have
    6x + 2y + 4 + 6 = 0
    Finally, the equation of the line is
    6x + 2y + 10 = 0
    Dividing the equation throughout by2, we get
    3x + y + 5 = 0
    This is the general form of the equation.
    This is also the required equation.
    Note:
    We can simplify the equation in any other way and we would still reach the same equation. The general form of an equation in two variables is given by ax + by + c = 0, where a, b, c are real numbers. The student is advised to remember all the different forms of a line, like, slope-intercept form, axis-intercept form, etc.

    Write equation of the line containing (-3, 4) and (-1, -2)

    Maths-General
    Hint:
    We are given two points and we need to find the equation of the line passing through them. Recall that the equation of a line passing through two points (a, b) and (c, d) is given by
    Step by step solution:
    Let the given points be denoted by
    (a, b) = (-3, 4)
    (c, d) = (-1, -2)
    The equation of a line passing through two points (a, b) and (c, d) is
    fraction numerator y minus d over denominator d minus b end fraction equals fraction numerator x minus c over denominator c minus a end fraction
    Using the above points, we have
    fraction numerator y minus left parenthesis negative 2 right parenthesis over denominator negative 2 minus 4 end fraction equals fraction numerator x minus left parenthesis negative 1 right parenthesis over denominator negative 1 minus left parenthesis negative 3 right parenthesis end fraction
    Simplifying the above equation, we have
    fraction numerator y plus 2 over denominator negative 6 end fraction equals fraction numerator x plus 1 over denominator negative 1 plus 3 end fraction
    not stretchy rightwards double arrow fraction numerator y plus 2 over denominator negative 6 end fraction equals fraction numerator x plus 1 over denominator 2 end fraction
    Cross multiplying, we get
    2(y + 2) = -6(x + 1)
    Expanding the factors, we have
    2y + 4 = -6x - 6
    Taking all the terms in the left hand side, we have
    6x + 2y + 4 + 6 = 0
    Finally, the equation of the line is
    6x + 2y + 10 = 0
    Dividing the equation throughout by2, we get
    3x + y + 5 = 0
    This is the general form of the equation.
    This is also the required equation.
    Note:
    We can simplify the equation in any other way and we would still reach the same equation. The general form of an equation in two variables is given by ax + by + c = 0, where a, b, c are real numbers. The student is advised to remember all the different forms of a line, like, slope-intercept form, axis-intercept form, etc.
    General
    Maths-

    Simplify and write the polynomial in its standard form.
    open parentheses 3 x squared minus 5 x minus 8 close parentheses minus open parentheses negative 4 x squared minus 2 x minus 1 close parentheses

    Explanation:
    • We have been given a function in the question.
    • We will have to simplify it and further write the answer in its standard form
    Step 1 of 1:
    We know that in polynomial we add/subtract like terms
    So,
    open parentheses 3 x squared minus 5 x minus 8 close parentheses minus open parentheses negative 4 x squared minus 2 x minus 1 close parentheses
    7 x squared minus 3 x minus 7
    Now, We know that the terms are written in descending order of their degree.
    So, In the standard form
    The given polynomial will be 7 x squared minus 3 x minus 7.

    Simplify and write the polynomial in its standard form.
    open parentheses 3 x squared minus 5 x minus 8 close parentheses minus open parentheses negative 4 x squared minus 2 x minus 1 close parentheses

    Maths-General
    Explanation:
    • We have been given a function in the question.
    • We will have to simplify it and further write the answer in its standard form
    Step 1 of 1:
    We know that in polynomial we add/subtract like terms
    So,
    open parentheses 3 x squared minus 5 x minus 8 close parentheses minus open parentheses negative 4 x squared minus 2 x minus 1 close parentheses
    7 x squared minus 3 x minus 7
    Now, We know that the terms are written in descending order of their degree.
    So, In the standard form
    The given polynomial will be 7 x squared minus 3 x minus 7.
    General
    Maths-

    What must be added to x3+3x-8 to get 3x3+x2+6?

    Answer:
    • Hint:
    ○     Addition of polynomials.
    ○     Always take like terms together while performing addition.
    ○     In addition to polynomials only terms with the same coefficient are added.
    • Step by step explanation:
    ○     Given:
    Sum:  3x3 + x2 + 6
    Term : x3 + 3x - 8
    ○     Step 1:
    ○      Let A must be added to get 3x3 + x2 + 6.
    So,
    rightwards double arrow A + x3 + 3x - 8 = 3x3 + x2 + 6
    rightwards double arrow A = (3x3 + x2 + 6 ) - (x3 + 3x - 8)
    rightwards double arrow A = 3x3 + x2 + 6 - x3 - 3x + 8
    rightwards double arrow A = 3x3- x3 + x2 - 3x+ 6 + 8
    rightwards double arrow A = 2x3 + x2 - 3x+ 14
    • Final Answer:
    Hence, the other term is 2x3 + x2 - 3x+ 14.

    What must be added to x3+3x-8 to get 3x3+x2+6?

    Maths-General
    Answer:
    • Hint:
    ○     Addition of polynomials.
    ○     Always take like terms together while performing addition.
    ○     In addition to polynomials only terms with the same coefficient are added.
    • Step by step explanation:
    ○     Given:
    Sum:  3x3 + x2 + 6
    Term : x3 + 3x - 8
    ○     Step 1:
    ○      Let A must be added to get 3x3 + x2 + 6.
    So,
    rightwards double arrow A + x3 + 3x - 8 = 3x3 + x2 + 6
    rightwards double arrow A = (3x3 + x2 + 6 ) - (x3 + 3x - 8)
    rightwards double arrow A = 3x3 + x2 + 6 - x3 - 3x + 8
    rightwards double arrow A = 3x3- x3 + x2 - 3x+ 6 + 8
    rightwards double arrow A = 2x3 + x2 - 3x+ 14
    • Final Answer:
    Hence, the other term is 2x3 + x2 - 3x+ 14.
    parallel
    General
    Maths-

    Simplify and write the polynomial in its standard form.
    open parentheses x squared plus 2 x minus 4 close parentheses plus open parentheses 2 x squared minus 5 x minus 3 close parentheses

    Explanation:
    • We have been given a function in the question.
    • We will have to simplify it and further write the answer in its standard form
    Step 1 of 1:
    We know that in polynomial we add/subtract like terms
    So,
    open parentheses x squared plus 2 x minus 4 close parentheses plus open parentheses 2 x squared minus 5 x minus 3 close parentheses
    3 x squared minus 3 x minus 7
    Now, We know that the terms are written in descending order of their degree.
    So, In the standard form
    The given polynomial will be 3 x squared minus 3 x minus 7.

    Simplify and write the polynomial in its standard form.
    open parentheses x squared plus 2 x minus 4 close parentheses plus open parentheses 2 x squared minus 5 x minus 3 close parentheses

    Maths-General
    Explanation:
    • We have been given a function in the question.
    • We will have to simplify it and further write the answer in its standard form
    Step 1 of 1:
    We know that in polynomial we add/subtract like terms
    So,
    open parentheses x squared plus 2 x minus 4 close parentheses plus open parentheses 2 x squared minus 5 x minus 3 close parentheses
    3 x squared minus 3 x minus 7
    Now, We know that the terms are written in descending order of their degree.
    So, In the standard form
    The given polynomial will be 3 x squared minus 3 x minus 7.
    General
    Maths-

    Write the polynomial in its standard form.
    2 y minus 3 minus y squared

    Explanation:
    • We have been given a function in the question.
    • We will have to simplify it and further write the answer in its standard form.
    Step 1 of 1:
    We have given a polynomial 2 y minus 3 minus y squared
    We know that the terms are written in descending order of their degree.
    So, In Standard form
    negative y squared plus 2 y minus 3

    Write the polynomial in its standard form.
    2 y minus 3 minus y squared

    Maths-General
    Explanation:
    • We have been given a function in the question.
    • We will have to simplify it and further write the answer in its standard form.
    Step 1 of 1:
    We have given a polynomial 2 y minus 3 minus y squared
    We know that the terms are written in descending order of their degree.
    So, In Standard form
    negative y squared plus 2 y minus 3
    General
    Maths-

    Name the polynomial based on its degree and number of terms.
    x over 4 plus 2

    • We have been given a function in the question
    • We will have to name the polynomial based on its degree and number of terms.
    Step 1 of 1:
    We have given a polynomial x over 4 plus 2
    Its degree is 1 and contain one variable
    This is linear polynomial

    Name the polynomial based on its degree and number of terms.
    x over 4 plus 2

    Maths-General
    • We have been given a function in the question
    • We will have to name the polynomial based on its degree and number of terms.
    Step 1 of 1:
    We have given a polynomial x over 4 plus 2
    Its degree is 1 and contain one variable
    This is linear polynomial
    parallel
    General
    Maths-

    Show m = 2 for the straight line 8x - 4y = 12.

    Hint:
    We need to verify the value of m for an equation of straight line. We take the help of slope intercept form of equation of a line and convert the given equation in the form y = mx + c. Then we compare both the equations to find the value of m and check if it is equal to the given value.
    Step by step solution:
    The slope/ gradient of a line is denoted by m.
    The given equation of the line is
    8x - 4y = 12
    We convert this equation in the slope intercept form, which is
    y = mx + c
    Where m is the slope of the line and c is the y-intercept.
    We rewrite the equation 8x - 4y = 12, as below
    -4y = -8x - 12
    Dividing the above equation by (-4) throughout, we get
    fraction numerator negative 4 over denominator negative 4 end fraction y equals fraction numerator negative 8 over denominator negative 4 end fraction x minus fraction numerator 12 over denominator negative 4 end fraction
    Simplifying, we have
    y = 2x + 3
    Comparing with y = mx + c, we get that m = 2
    Thus, m = 2 for the straight line 8x - 4y = 12
    Note:
    We can find the slope and y-intercept directly from the general form of the equation too; slope =negative straight a over straight b  and y-intercept = c over b, where the general form of equation of a line is ax + by + c = 0. Using this method, be careful to check that the equation is in general form before applying the formula. Here, we have, a = 8, b = -4, so we get m equals negative fraction numerator 8 over denominator negative 4 end fraction equals 2

    Show m = 2 for the straight line 8x - 4y = 12.

    Maths-General
    Hint:
    We need to verify the value of m for an equation of straight line. We take the help of slope intercept form of equation of a line and convert the given equation in the form y = mx + c. Then we compare both the equations to find the value of m and check if it is equal to the given value.
    Step by step solution:
    The slope/ gradient of a line is denoted by m.
    The given equation of the line is
    8x - 4y = 12
    We convert this equation in the slope intercept form, which is
    y = mx + c
    Where m is the slope of the line and c is the y-intercept.
    We rewrite the equation 8x - 4y = 12, as below
    -4y = -8x - 12
    Dividing the above equation by (-4) throughout, we get
    fraction numerator negative 4 over denominator negative 4 end fraction y equals fraction numerator negative 8 over denominator negative 4 end fraction x minus fraction numerator 12 over denominator negative 4 end fraction
    Simplifying, we have
    y = 2x + 3
    Comparing with y = mx + c, we get that m = 2
    Thus, m = 2 for the straight line 8x - 4y = 12
    Note:
    We can find the slope and y-intercept directly from the general form of the equation too; slope =negative straight a over straight b  and y-intercept = c over b, where the general form of equation of a line is ax + by + c = 0. Using this method, be careful to check that the equation is in general form before applying the formula. Here, we have, a = 8, b = -4, so we get m equals negative fraction numerator 8 over denominator negative 4 end fraction equals 2
    General
    Maths-

    Simplify. Write each answer in its standard form.
    left parenthesis negative 5 x minus 6 right parenthesis minus open parentheses 4 x squared plus 6 close parentheses

    Explanation:
    • We have been given a function in the question.
    • We will have to simplify it and further write the answer in its standard form.
    Step 1 of 1:
    We know that in polynomial we add/subtract like terms
    So,
    left parenthesis negative 5 x minus 6 right parenthesis minus open parentheses 4 x squared plus 6 close parentheses
    negative 4 x squared minus 5 x minus 12
    Now, We know that the terms are written in descending order of their degree.
    So, In the standard form
    The given polynomial will be negative 4 x squared minus 5 x minus 12.

    Simplify. Write each answer in its standard form.
    left parenthesis negative 5 x minus 6 right parenthesis minus open parentheses 4 x squared plus 6 close parentheses

    Maths-General
    Explanation:
    • We have been given a function in the question.
    • We will have to simplify it and further write the answer in its standard form.
    Step 1 of 1:
    We know that in polynomial we add/subtract like terms
    So,
    left parenthesis negative 5 x minus 6 right parenthesis minus open parentheses 4 x squared plus 6 close parentheses
    negative 4 x squared minus 5 x minus 12
    Now, We know that the terms are written in descending order of their degree.
    So, In the standard form
    The given polynomial will be negative 4 x squared minus 5 x minus 12.
    General
    Maths-

    Simplify. Write each answer in its standard form.
    open parentheses 3 x squared plus 4 x plus 2 close parentheses minus left parenthesis negative x plus 4 right parenthesis

    Explanation:
    • We have been given a function in the question.
    • We will have to simplify it and further write the answer in its standard form.
    Step 1 of 1:
    We know that in polynomial we add/subtract like terms
    So,
    open parentheses 3 x squared plus 4 x plus 2 close parentheses minus left parenthesis negative x plus 4 right parenthesis
    open parentheses 3 x squared plus 5 x minus 2 close parentheses
    Now, We know that the terms are written in descending order of their degree.
    So, In the standard form
    The given polynomial will be open parentheses 3 x squared plus 5 x minus 2 close parentheses

    Simplify. Write each answer in its standard form.
    open parentheses 3 x squared plus 4 x plus 2 close parentheses minus left parenthesis negative x plus 4 right parenthesis

    Maths-General
    Explanation:
    • We have been given a function in the question.
    • We will have to simplify it and further write the answer in its standard form.
    Step 1 of 1:
    We know that in polynomial we add/subtract like terms
    So,
    open parentheses 3 x squared plus 4 x plus 2 close parentheses minus left parenthesis negative x plus 4 right parenthesis
    open parentheses 3 x squared plus 5 x minus 2 close parentheses
    Now, We know that the terms are written in descending order of their degree.
    So, In the standard form
    The given polynomial will be open parentheses 3 x squared plus 5 x minus 2 close parentheses
    parallel
    General
    Maths-

    Simplify -6 + 4a2 + 2b2 - 7xz - 3xz + 4a2 - 5b2 - 2.

    Answer:
    • Hint:
    ○        Group the like terms.
    ○        Like terms are those whose coefficients are the same.
    ○        Perform basic arithmetic operations on like terms.
    • Step by step explanation:
    ○        Given:
    Expression: -6 + 4a2 + 2b2 - 7xz - 3xz + 4a2 - 5b2 - 2.
    ○        Step 1:
    ○        Group like terms.
    rightwards double arrow-6 + 4a2 + 2b2 - 7xz - 3xz + 4a2 - 5b2 - 2
    rightwards double arrow( -6 - 2) + (4a2 + 4a2) - (7xz + 3xz) + (2b2 - 5b2 )
    rightwards double arrow( -8) + (8a2) - (10xz ) + (- 3b2 )
    rightwards double arrow 8a2 - 3b2 - 10xz - 8
    • Final Answer:
    Hence, the other term is 8a2 - 3b2 - 10xz - 8.

    Simplify -6 + 4a2 + 2b2 - 7xz - 3xz + 4a2 - 5b2 - 2.

    Maths-General
    Answer:
    • Hint:
    ○        Group the like terms.
    ○        Like terms are those whose coefficients are the same.
    ○        Perform basic arithmetic operations on like terms.
    • Step by step explanation:
    ○        Given:
    Expression: -6 + 4a2 + 2b2 - 7xz - 3xz + 4a2 - 5b2 - 2.
    ○        Step 1:
    ○        Group like terms.
    rightwards double arrow-6 + 4a2 + 2b2 - 7xz - 3xz + 4a2 - 5b2 - 2
    rightwards double arrow( -6 - 2) + (4a2 + 4a2) - (7xz + 3xz) + (2b2 - 5b2 )
    rightwards double arrow( -8) + (8a2) - (10xz ) + (- 3b2 )
    rightwards double arrow 8a2 - 3b2 - 10xz - 8
    • Final Answer:
    Hence, the other term is 8a2 - 3b2 - 10xz - 8.
    General
    Maths-

    open parentheses 4 x squared plus 2 x minus 3 close parentheses plus open parentheses 3 x squared plus 6 close parentheses

    Explanation:
    • We have been given a function in the question.
    • We have to simplify it and further writer it in its standard form.
    Step 1 of 1:
    We know that in polynomial we add/subtract like terms
    So,
    open parentheses 4 x squared plus 2 x minus 3 close parentheses plus open parentheses 3 x squared plus 6 close parentheses
    7 x squared plus 2 x plus 3
    Now, We know that the terms are written in descending order of their degree.
    So, In the standard form
    The given polynomial will be 7 x squared plus 2 x plus 3.

    open parentheses 4 x squared plus 2 x minus 3 close parentheses plus open parentheses 3 x squared plus 6 close parentheses

    Maths-General
    Explanation:
    • We have been given a function in the question.
    • We have to simplify it and further writer it in its standard form.
    Step 1 of 1:
    We know that in polynomial we add/subtract like terms
    So,
    open parentheses 4 x squared plus 2 x minus 3 close parentheses plus open parentheses 3 x squared plus 6 close parentheses
    7 x squared plus 2 x plus 3
    Now, We know that the terms are written in descending order of their degree.
    So, In the standard form
    The given polynomial will be 7 x squared plus 2 x plus 3.
    General
    Maths-

    The coordinate A=(0,2) lies on a straight line. The gradient of the line is 5 . Using this information, state the equation of the straight line.

    Hint:
    We are given the slope of a line and a point which lies on the straight line. To find the equation of the line, we use the point slope form of the equation which is given by y - b = m(x - a), where m is the slope and (a, b) is the point lying on the plane. We simplify this equation and bring it to the general form which is ax + by + c = 0
    Step by step solution:
    Given,
    Slope/ Gradient of the line (m) = 5
    Let (a, b) denote the point A lying on the plane.
    Then (a, b) = (0, 2)
    We know that, the equation of a line with slope m and passing through the point (a, b) is given by
    y - b = m(x - a)
    Putting the values of m and (a, b) in the above equation, we get
    y - 2 = 5(x - 0)
    Simplifying, we have
    y - 2 = 5x
    Taking all the terms on one side and rewriting the above equation, we have
    5x - y + 2 = 0
    This is the required equation of the line.
    Note:
    The student needs to remember all the different forms of equation of a line and what each term and notation signifies in the equation.
    Other forms of the equation of a line are, slope intercept form, axis intercept form, normal form, etc.

    The coordinate A=(0,2) lies on a straight line. The gradient of the line is 5 . Using this information, state the equation of the straight line.

    Maths-General
    Hint:
    We are given the slope of a line and a point which lies on the straight line. To find the equation of the line, we use the point slope form of the equation which is given by y - b = m(x - a), where m is the slope and (a, b) is the point lying on the plane. We simplify this equation and bring it to the general form which is ax + by + c = 0
    Step by step solution:
    Given,
    Slope/ Gradient of the line (m) = 5
    Let (a, b) denote the point A lying on the plane.
    Then (a, b) = (0, 2)
    We know that, the equation of a line with slope m and passing through the point (a, b) is given by
    y - b = m(x - a)
    Putting the values of m and (a, b) in the above equation, we get
    y - 2 = 5(x - 0)
    Simplifying, we have
    y - 2 = 5x
    Taking all the terms on one side and rewriting the above equation, we have
    5x - y + 2 = 0
    This is the required equation of the line.
    Note:
    The student needs to remember all the different forms of equation of a line and what each term and notation signifies in the equation.
    Other forms of the equation of a line are, slope intercept form, axis intercept form, normal form, etc.
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