Maths-
General
Easy

Question

Write the product in the standard form. (𝑥 − 2.5)(𝑥 + 2.5)

Hint:

The methods used to find the product of binomials are called special products.
Difference of squares is a case of a special product which occurs when we multiply a binomial by another binomial with the same terms but the opposite sign

The correct answer is: 6.25.


    (x − 2.5)(x + 2.5) = (x − 5 over 2)(x + 5 over 2)

    = x(x + 5 over 2) - 5 over 2(x + 5 over 2)

    =  x(x) + x(5 over 2) - 5 over 2(x) - 5 over 2(5 over 2)

    = x2 + 5 over 2x - 5 over 2x -25 over 4

    = x225 over 4

    = x2 - 6.25
    Final Answer:
    Hence, the simplified form of (𝑥 − 2.5)(𝑥 + 2.5) is x2 - 6.25.
     

    This question can be easily solved by using the formula
    (a + b)(a - b) = a2 - b2

    Related Questions to study

    General
    Maths-

    Describe the possible lengths of the third side of the triangle given the lengths of the other two sides.
    5 inches, 12 inches

    Answer:
    • Hints:

      • Triangle inequality theorem
      • According to this theorem, in any triangle, sum of two sides is greater than third side,
      • a < b + c
    b < a + c
    c < a + b
      • while finding possible lengths of third side use below formula
    difference of two side < third side < sum of two sides
    • Step-by-step explanation: 

      • Given:
    In triangle, sides are 5 inches and 12 inches.
    a = 5 inches, b = 12 inches.
    • Step-by-step explanation: 

      • Given:
    In triangle, sides are 5 inches and 12 inches.
    a = 5 inches, b = 12 inches.
      • Step 1:
      • Find length of third side.
    According to triangle inequality theorem,
    c < a + b
    ∴ c < 5 + 12
    c < 17
      • Step 1:
      • Find length of third side.
    According to triangle inequality theorem,
    c < a + b
    ∴ c < 5 + 12
    c < 17
      • Step 2:
    difference of two side < third side < sum of two sides
      • Step 2:
    b – a < c < a + b
    12 – 5 < c < 5 + 12
    7 < c < 17
    Hence, all numbers between 7 and 17 will be the length of third side.
    • Final Answer: 
    Hence, all numbers between 7 and 17 will be the length of third side.



     

    Describe the possible lengths of the third side of the triangle given the lengths of the other two sides.
    5 inches, 12 inches

    Maths-General
    Answer:
    • Hints:

      • Triangle inequality theorem
      • According to this theorem, in any triangle, sum of two sides is greater than third side,
      • a < b + c
    b < a + c
    c < a + b
      • while finding possible lengths of third side use below formula
    difference of two side < third side < sum of two sides
    • Step-by-step explanation: 

      • Given:
    In triangle, sides are 5 inches and 12 inches.
    a = 5 inches, b = 12 inches.
    • Step-by-step explanation: 

      • Given:
    In triangle, sides are 5 inches and 12 inches.
    a = 5 inches, b = 12 inches.
      • Step 1:
      • Find length of third side.
    According to triangle inequality theorem,
    c < a + b
    ∴ c < 5 + 12
    c < 17
      • Step 1:
      • Find length of third side.
    According to triangle inequality theorem,
    c < a + b
    ∴ c < 5 + 12
    c < 17
      • Step 2:
    difference of two side < third side < sum of two sides
      • Step 2:
    b – a < c < a + b
    12 – 5 < c < 5 + 12
    7 < c < 17
    Hence, all numbers between 7 and 17 will be the length of third side.
    • Final Answer: 
    Hence, all numbers between 7 and 17 will be the length of third side.



     
    General
    Maths-

    Write the product in the standard form. (3𝑎 − 4𝑏)(3𝑎 + 4𝑏)

    (3a − 4b)(3a + 4b)  = 3a(3a + 4b) - 4b(3a + 4b)
    =  3a(3a) + 3a(4b) - 4b(3a) - 4b(4b)
    = 9a2 + 12ab - 12ab - 16b2
    = 9a2 - 16b2
    Final Answer:
    Hence, the simplified form of (3𝑎 − 4𝑏)(3𝑎 + 4𝑏) is 9a2 - 16b2.
     

    Write the product in the standard form. (3𝑎 − 4𝑏)(3𝑎 + 4𝑏)

    Maths-General
    (3a − 4b)(3a + 4b)  = 3a(3a + 4b) - 4b(3a + 4b)
    =  3a(3a) + 3a(4b) - 4b(3a) - 4b(4b)
    = 9a2 + 12ab - 12ab - 16b2
    = 9a2 - 16b2
    Final Answer:
    Hence, the simplified form of (3𝑎 − 4𝑏)(3𝑎 + 4𝑏) is 9a2 - 16b2.
     
    General
    Maths-

    Write the product in the standard form. open parentheses 1 fourth x minus 2 over 3 close parentheses open parentheses 1 fourth x plus 2 over 3 close parentheses

    open parentheses 1 fourth x minus 2 over 3 close parentheses open parentheses 1 fourth x plus 2 over 3 close parentheses equals 1 fourth x open parentheses 1 fourth x plus 2 over 3 close parentheses minus 2 over 3 open parentheses 1 fourth x plus 2 over 3 close parentheses

    equals 1 fourth x open parentheses 1 fourth x close parentheses plus 1 fourth x open parentheses 2 over 3 close parentheses minus 2 over 3 open parentheses 1 fourth x close parentheses minus 2 over 3 open parentheses 2 over 3 close parentheses

    equals 1 over 16 x squared plus 1 over 6 x minus 1 over 6 x minus 4 over 9
    equals 1 over 16 x squared minus 4 over 9
    Final Answer:
    Hence, the simplified form of open parentheses 1 fourth x minus 2 over 3 close parentheses open parentheses 1 fourth x plus 2 over 3 close parentheses text  is  end text 1 over 16 x squared minus 4 over 9.
     

    Write the product in the standard form. open parentheses 1 fourth x minus 2 over 3 close parentheses open parentheses 1 fourth x plus 2 over 3 close parentheses

    Maths-General
    open parentheses 1 fourth x minus 2 over 3 close parentheses open parentheses 1 fourth x plus 2 over 3 close parentheses equals 1 fourth x open parentheses 1 fourth x plus 2 over 3 close parentheses minus 2 over 3 open parentheses 1 fourth x plus 2 over 3 close parentheses

    equals 1 fourth x open parentheses 1 fourth x close parentheses plus 1 fourth x open parentheses 2 over 3 close parentheses minus 2 over 3 open parentheses 1 fourth x close parentheses minus 2 over 3 open parentheses 2 over 3 close parentheses

    equals 1 over 16 x squared plus 1 over 6 x minus 1 over 6 x minus 4 over 9
    equals 1 over 16 x squared minus 4 over 9
    Final Answer:
    Hence, the simplified form of open parentheses 1 fourth x minus 2 over 3 close parentheses open parentheses 1 fourth x plus 2 over 3 close parentheses text  is  end text 1 over 16 x squared minus 4 over 9.
     

    parallel
    General
    Maths-

    How is it possible that the sum of two quadratic trinomials is a linear binomial?

    Explanation:
    • We have to find out how is it possible that the sum of two quadratic trinomials is a linear binomial.
    Step 1 of 1:
    it is possible that the sum of two quadratic trinomials is a linear binomial
    If the other terms get cancel
    Example:
    2 x squared plus 5 x minus 3,
    negative 2 x squared minus 2 x plus 5
    On addition we will get 3 x plus 2, which is a linear binomial.

    How is it possible that the sum of two quadratic trinomials is a linear binomial?

    Maths-General
    Explanation:
    • We have to find out how is it possible that the sum of two quadratic trinomials is a linear binomial.
    Step 1 of 1:
    it is possible that the sum of two quadratic trinomials is a linear binomial
    If the other terms get cancel
    Example:
    2 x squared plus 5 x minus 3,
    negative 2 x squared minus 2 x plus 5
    On addition we will get 3 x plus 2, which is a linear binomial.
    General
    Maths-

    If (3x-4) (5x+7) = 15x2-ax-28, so find the value of a?

    Answer:
    • Hint:
    ○     While evaluating the expression just put the values and perform basic operations.
    • Step by step explanation:
    ○     Given:
    ○     Two terms.
    (3x-4) (5x+7) = 15x2-ax-28
    ○     Step 1:
    ○     Simplify the right side:
    ○     (3x-4) (5x+7)
    rightwards double arrow 3x(5x+7) - 4(5x+7)
    rightwards double arrow15x2 + 21x - 20x - 28
    rightwards double arrow15x2 + x - 28
    ○     Step 1:
    ○     compare both side:
    15x2 + x - 28 =15x2- ax - 28
    By comparing we get
    a = -1
    • Final Answer:
    Hence, the value a is -1.

    If (3x-4) (5x+7) = 15x2-ax-28, so find the value of a?

    Maths-General
    Answer:
    • Hint:
    ○     While evaluating the expression just put the values and perform basic operations.
    • Step by step explanation:
    ○     Given:
    ○     Two terms.
    (3x-4) (5x+7) = 15x2-ax-28
    ○     Step 1:
    ○     Simplify the right side:
    ○     (3x-4) (5x+7)
    rightwards double arrow 3x(5x+7) - 4(5x+7)
    rightwards double arrow15x2 + 21x - 20x - 28
    rightwards double arrow15x2 + x - 28
    ○     Step 1:
    ○     compare both side:
    15x2 + x - 28 =15x2- ax - 28
    By comparing we get
    a = -1
    • Final Answer:
    Hence, the value a is -1.
    General
    Maths-

    The difference of x4+2x2-3x+7 and another polynomial is x3+x2+x-1. What is the
    another polynomial?

    Answer:
    • Hint:
    ○    Subtraction of polynomials.
    ○     Always take like terms together while performing subtraction.
    ○     In addition to polynomials only terms with the same coefficient are subtracted.
    • Step by step explanation:
    ○    Given:
    One polynomial: x4+2x2-3x+7
    Difference: x3+x2+x-1.
    ○     Step 1:
    ○     Let another polynomial be A.
    So,
    rightwards double arrow(x4+2x2-3x+7) – A = (x3+x2+x-1)
    rightwards double arrowA = (x4+2x2-3x+7) - (x3+x2+x-1)
    rightwards double arrow A = x4 + 2x2 - 3x + 7 - x3 - x2 - x + 1
    rightwards double arrow A = x4- x3 + 2x2- x2 - 3x - x + 7 + 1
    rightwards double arrow A = x4 - x3 + x2 - 4x + 8
    • Final Answer:
    Hence, another polynomial is x4 - x3 + x2 - 4x + 8.

    The difference of x4+2x2-3x+7 and another polynomial is x3+x2+x-1. What is the
    another polynomial?

    Maths-General
    Answer:
    • Hint:
    ○    Subtraction of polynomials.
    ○     Always take like terms together while performing subtraction.
    ○     In addition to polynomials only terms with the same coefficient are subtracted.
    • Step by step explanation:
    ○    Given:
    One polynomial: x4+2x2-3x+7
    Difference: x3+x2+x-1.
    ○     Step 1:
    ○     Let another polynomial be A.
    So,
    rightwards double arrow(x4+2x2-3x+7) – A = (x3+x2+x-1)
    rightwards double arrowA = (x4+2x2-3x+7) - (x3+x2+x-1)
    rightwards double arrow A = x4 + 2x2 - 3x + 7 - x3 - x2 - x + 1
    rightwards double arrow A = x4- x3 + 2x2- x2 - 3x - x + 7 + 1
    rightwards double arrow A = x4 - x3 + x2 - 4x + 8
    • Final Answer:
    Hence, another polynomial is x4 - x3 + x2 - 4x + 8.
    parallel
    General
    Maths-

    Use the product of sum and difference to find 83 × 97.

    83 can be written as (90 - 7) and 97 can be written as (90 + 7)
    So, 83 × 97 can be written (90 - 7) ×  (90 + 7)
    (90 - 7) ×  (90 + 7)  = 90(90 + 7) - 7(90 + 7)

    =  90(90) + 90(7) - 7(90) - 7(7)

    = 8100 + 630 - 630 - 49

    = 8100 - 49

    = 8051
    Final Answer:
    Hence, the simplified form of 83 × 97 is 8051.
     

    Use the product of sum and difference to find 83 × 97.

    Maths-General
    83 can be written as (90 - 7) and 97 can be written as (90 + 7)
    So, 83 × 97 can be written (90 - 7) ×  (90 + 7)
    (90 - 7) ×  (90 + 7)  = 90(90 + 7) - 7(90 + 7)

    =  90(90) + 90(7) - 7(90) - 7(7)

    = 8100 + 630 - 630 - 49

    = 8100 - 49

    = 8051
    Final Answer:
    Hence, the simplified form of 83 × 97 is 8051.
     

    General
    Maths-

    Determine the gradient and y-intercept from the following equation: 4x + y = -10

    Hint:
    Gradient is also called the slope of the line. The slope intercept form of the equation of the line is y = mx + c, where m is the slope of the line and c is the y-intercept. First we convert the given equation in this form. Further, we compare the equation with the standard form to get the slope and the y-intercept.
    Step by step solution:
    The given equation of the line is
    4x + y = -10
    We need to convert this equation in the slope-intercept form of the line, which is
    y = mx + c, where m is the slope of the line and c is the y – intercept.
    Rewriting the given equation, that is, keeping only the term containing y in the left hand side, we get
    y = -4x - 10
    Comparing the above equation with y = mx + c, we get
    m = -4 ;c = -10
    Thus, we get
    Gradient = -4
    y-intercept = -10
    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.

    Determine the gradient and y-intercept from the following equation: 4x + y = -10

    Maths-General
    Hint:
    Gradient is also called the slope of the line. The slope intercept form of the equation of the line is y = mx + c, where m is the slope of the line and c is the y-intercept. First we convert the given equation in this form. Further, we compare the equation with the standard form to get the slope and the y-intercept.
    Step by step solution:
    The given equation of the line is
    4x + y = -10
    We need to convert this equation in the slope-intercept form of the line, which is
    y = mx + c, where m is the slope of the line and c is the y – intercept.
    Rewriting the given equation, that is, keeping only the term containing y in the left hand side, we get
    y = -4x - 10
    Comparing the above equation with y = mx + c, we get
    m = -4 ;c = -10
    Thus, we get
    Gradient = -4
    y-intercept = -10
    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.
    General
    Maths-

    Use the product of sum and difference to find 32 × 28.

    32 can be written as (30 + 2) and 28 can be written as (30 - 2)
    So, 32 × 28 can be written (30 + 2) ×  (30 - 2)
    (30 + 2) ×  (30 - 2)  = 30(30 - 2) + 2(30 - 2)

    =  30(30) + 30(-2) + 2(30) + 2(-2)

    = 900 - 60 + 60 - 4

    = 900 - 4

    = 896
    Final Answer:
    Hence, the simplified form of 32 × 28 is 896.
     

    Use the product of sum and difference to find 32 × 28.

    Maths-General
    32 can be written as (30 + 2) and 28 can be written as (30 - 2)
    So, 32 × 28 can be written (30 + 2) ×  (30 - 2)
    (30 + 2) ×  (30 - 2)  = 30(30 - 2) + 2(30 - 2)

    =  30(30) + 30(-2) + 2(30) + 2(-2)

    = 900 - 60 + 60 - 4

    = 900 - 4

    = 896
    Final Answer:
    Hence, the simplified form of 32 × 28 is 896.
     

    parallel
    General
    Maths-

    The sum of two expressions is x3-x2+3x-2. If one of them is x2 + 5x - 6, what is the
    other?

    Answer:
    • Hint:
    ○      Addition of polynomials.
    ○      Always take like terms together while performing addition.
    ○      In subtraction of polynomials only coefficients are subtracted.
    • Step by step explanation:
    ○      Given:
    Sum:  x3 -x2 + 3x- 2
    Term: x2 + 5x- 6
    ○      Step 1:
    ○      Let the other term be A.
    As given sum is x3 -x2 + 3x- 2
    rightwards double arrow A + x2 + 5x- 6 = x3 -x2 + 3x- 2
    rightwards double arrow A = x3 -x2 + 3x- 2 ) - ( x2 + 5x- 6 )
    rightwards double arrow A = x3 -x2 + 3x - 2 - x2 - 5x + 6
    rightwards double arrow A = x3 -x2 - x2 + 3x - 5x - 2 + 6
    rightwards double arrow A = x3 -2x2 - 2x + 4
    • Final Answer:
    Hence, the other term is x3 -2x2 - 2x + 4.

    The sum of two expressions is x3-x2+3x-2. If one of them is x2 + 5x - 6, what is the
    other?

    Maths-General
    Answer:
    • Hint:
    ○      Addition of polynomials.
    ○      Always take like terms together while performing addition.
    ○      In subtraction of polynomials only coefficients are subtracted.
    • Step by step explanation:
    ○      Given:
    Sum:  x3 -x2 + 3x- 2
    Term: x2 + 5x- 6
    ○      Step 1:
    ○      Let the other term be A.
    As given sum is x3 -x2 + 3x- 2
    rightwards double arrow A + x2 + 5x- 6 = x3 -x2 + 3x- 2
    rightwards double arrow A = x3 -x2 + 3x- 2 ) - ( x2 + 5x- 6 )
    rightwards double arrow A = x3 -x2 + 3x - 2 - x2 - 5x + 6
    rightwards double arrow A = x3 -x2 - x2 + 3x - 5x - 2 + 6
    rightwards double arrow A = x3 -2x2 - 2x + 4
    • Final Answer:
    Hence, the other term is x3 -2x2 - 2x + 4.
    General
    Maths-

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

    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.

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

    Maths-General
    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.

    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
    parallel
    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.
    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.
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