Question

the points (-4, r) and (4, -4) lie on a line with slope -1. find the missing coordinate r.

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: Substitute known values

Let $(x_1,y_1)=(-4,r)$, $(x_2,y_2)=(4,-4)$, $m=-1$.
$$-1=\frac{-4 - r}{4 - (-4)}$$

Step3: Simplify denominator

$$-1=\frac{-4 - r}{8}$$

Step4: Solve for $r$

Multiply both sides by 8: $-8=-4 - r$
Add 4 to both sides: $-4=-r$
Multiply by $-1$: $r=4$

Answer:

4