Select all the correct answers.

The slope-intercept form of a line is $y=m x+b$, where $m$ is the slope and $b$ is the $y$-intercept. If Shawn knows that the slope of the line is 4 and the line passes through the point $(1,-8)$, which equation should he use to find the $y$-Intercept and what is the $y$-intercept of the line?

A. $b=y+m x$
B. $b=y-m x$
C. $b=\frac{y-m}{z}$
D. $b=-12$
E. $b=-4$
F. $b=2

The slope-intercept form is y = m x + b , and we need to find b .
Rearrange the equation to solve for b : b = y − m x .
Substitute the given values m = 4 , x = 1 , and y = − 8 into the equation.
Calculate b = − 8 − ( 4 ) ( 1 ) = − 12 , so the y-intercept is − 12 ​ .

Explanation

Understanding the Problem The slope-intercept form of a line is given by the equation y = m x + b , where m represents the slope and b represents the y-intercept. We are given that the slope m = 4 and the line passes through the point ( 1 , − 8 ) . This means that when x = 1 , y = − 8 . Our goal is to find the value of b , the y-intercept.

Finding the Equation for b To find the y-intercept, we need to rearrange the slope-intercept equation to solve for b . Starting with y = m x + b , we subtract m x from both sides to isolate b :


y − m x = b
So, b = y − m x .

Calculating the y-intercept Now, we substitute the given values m = 4 , x = 1 , and y = − 8 into the equation b = y − m x :

b = − 8 − ( 4 ) ( 1 )
b = − 8 − 4
b = − 12

Final Answer Therefore, the y-intercept of the line is -12. The correct equation to find the y-intercept is b = y − m x , and the y-intercept is b = − 12 .

Examples
Understanding the y-intercept is crucial in many real-world applications. For example, in a simple cost model, the equation y = m x + b might represent the total cost ( y ) of producing x items, where m is the cost per item and b is the fixed cost (the y-intercept). If you know the cost per item is 4 an d t h e t o t a l cos tt o p ro d u ce 1 i t e mi s " − 8" ( p er ha p s d u e t o a s u b s i d y ) , t h e n t h e f i x e d cos t sc anb ec a l c u l a t e d a s b = -8 - 4(1) = -12$. This means there's an initial credit or subsidy of $12, regardless of how many items are produced.

Answered by GinnyAnswer | 2025-07-04

To find the y-intercept b of the line given the slope m = 4 and the point ( 1 , − 8 ) , we rearranged the slope-intercept form y = m x + b to find b = y − m x . Substituting the values, we calculated b = − 12 . Therefore, the correct answers are B: b = y − m x and D: b = − 12 .
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Answered by Anonymous | 2025-07-14