Question
State the gradient and y-intercept of the line y = -3x + 8.
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. The given equation is already in this form. We compare the given equation with this form to get the slope and the y-intercept.
The correct answer is: we get Gradient = -3 y-intercept = 8
Step by step solution:
The given equation of the line is
y = - 3x + 8
Comparing the above equation with
y = mx + c
We get
m = -3; c = 8
Thus, we get
Gradient = -3
y-intercept = 8
Comparing the above equation with
We get
Thus, we get
The student needs to remember all the different forms of equation of a line and what each term and notation signifies in the equation.
We can find the slope and y-intercept directly from the general form of the equation too; slope = and y-intercept =
, where the general form of equation of a line is ax + by + c = 0.
Related Questions to study
In the standard form of a polynomial, the terms are written in ______order of their degree.
In the standard form of a polynomial, the terms are written in ______order of their degree.
Identify a binomial.
Identify a binomial.
What must be added to 5y2+3y + 1 to get 3y3 -7y2+8
What must be added to 5y2+3y + 1 to get 3y3 -7y2+8
Find the value of the y-intercept in the equation 3x-y+5=0.
Find the value of the y-intercept in the equation 3x-y+5=0.
𝐴𝑃 is perpendicular bisector of 𝐵𝐶.
1. What segment lengths are equal? Explain your reasoning.
2. Find AB.
3. Explain why D is on 𝐴𝑃.
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)
𝐴𝑃 is perpendicular bisector of 𝐵𝐶.
1. What segment lengths are equal? Explain your reasoning.
2. Find AB.
3. Explain why D is on 𝐴𝑃.
![](data:image/png;base64,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)
Identify a monomial.
Identify a monomial.
Convert the equation 5x + 4y = 12 into y = mx + c and find its y-intercept.
Convert the equation 5x + 4y = 12 into y = mx + c and find its y-intercept.
What must be subtracted from 3x2-5xy -2y2-3 to get 5x2-7xy -3y2+3x
What must be subtracted from 3x2-5xy -2y2-3 to get 5x2-7xy -3y2+3x
𝐴𝑃 is the perpendicular bisector of 𝐵𝐶.
a. What segment lengths in the diagram are equal?
b. Is A on 𝐴𝑃?
![](data:image/png;base64,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)
𝐴𝑃 is the perpendicular bisector of 𝐵𝐶.
a. What segment lengths in the diagram are equal?
b. Is A on 𝐴𝑃?
![](data:image/png;base64,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)
Use the square of a binomial to find the value. 562
Use the square of a binomial to find the value. 562
Is the given conjecture correct? Provide arguments to support your answer.
The product of any two consecutive odd numbers is 1 less than a perfect square.
Is the given conjecture correct? Provide arguments to support your answer.
The product of any two consecutive odd numbers is 1 less than a perfect square.
Name the polynomial based on its degree and number of terms.
![5 x y squared minus 3](data:image/png;base64,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)
Name the polynomial based on its degree and number of terms.
![5 x y squared minus 3](data:image/png;base64,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)
In an academic contest correct answers earn 12 points and incorrect answers lose 5
points. In the final round, school A starts with 165 points and gives the same number
of correct and incorrect answers. School B starts with 65 points and gives no incorrect answers and the same number of correct answers as school A. The game ends with the two schools tied.
ii)How many answers did each school get correct in the final round?
A linear equation in one variable is an equation that has only one solution and is expressed in the form ax+b = 0, where a and b are two integers and x is a variable. 2x+3=8, for example, is a linear equation with a single variable. As a result, this equation has only one solution, x = 5/2.
¶The standard form of a linear equation in one variable is: ax + b = 0
Where,
The letters 'a' and 'b' are real numbers.
'a' and 'b' are both greater than zero.
In an academic contest correct answers earn 12 points and incorrect answers lose 5
points. In the final round, school A starts with 165 points and gives the same number
of correct and incorrect answers. School B starts with 65 points and gives no incorrect answers and the same number of correct answers as school A. The game ends with the two schools tied.
ii)How many answers did each school get correct in the final round?
A linear equation in one variable is an equation that has only one solution and is expressed in the form ax+b = 0, where a and b are two integers and x is a variable. 2x+3=8, for example, is a linear equation with a single variable. As a result, this equation has only one solution, x = 5/2.
¶The standard form of a linear equation in one variable is: ax + b = 0
Where,
The letters 'a' and 'b' are real numbers.
'a' and 'b' are both greater than zero.