Question

the table shows a linear relationship between x and y. what is the rate of change of y with respect to x? a -\frac{9}{2} b \frac{2}{9} c -\frac{2}{9} d \frac{9}{2}

Explanation:

Step1: Recall slope formula

The rate of change of $y$ with respect to $x$ for a linear relationship is the slope $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points, say $(x_1,y_1)=(-20,96)$ and $(x_2,y_2)=(-12,60)$.

Step2: Substitute values into formula

$m=\frac{60 - 96}{-12-(-20)}=\frac{-36}{-12 + 20}=\frac{-36}{8}=-\frac{9}{2}$

Answer:

A. $-\frac{9}{2}$