line k passes through the points (-2, 5) and (4, -4) on the coordinate plane. what is the slope of line k?

Explanation:

Step1: Recall slope formula

The slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2-y_1}{x_2-x_1}$

Step2: Assign point values

Let $(x_1,y_1)=(-2,5)$ and $(x_2,y_2)=(4,-4)$

Step3: Substitute into slope formula

$m=\frac{-4-5}{4-(-2)}=\frac{-9}{6}$

Step4: Simplify the fraction

$m=-\frac{3}{2}$

Answer:

$-\frac{3}{2}$