Question

5 the table represents some points on the graph of a linear function. x -7.5 -3.5 -1 2 3.5 y 12 0 -7.5 -16.5 -21 which function represents the same relationship? a h(x)=-3x - 10.5 b h(x)=-x - 3.5 c h(x)=3x - 10.5 d h(x)=x - 3.5

Explanation:

Step1: Find the slope formula

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take the points $(-7.5,12)$ and $(-3.5,0)$. Then $m=\frac{0 - 12}{-3.5-(-7.5)}=\frac{- 12}{4}=-3$.

Step2: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Using the point $(-3.5,0)$ and $m = - 3$, we have $y-0=-3(x + 3.5)$.

Step3: Simplify the equation

Expand the right - hand side: $y=-3x-10.5$.

Answer:

A. $h(x)=-3x - 10.5$