Question

a line that includes the points (7, 4) and (z, -4) has a slope of 8. what is the value of z? z = submit

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: Plug in known values

Substitute $m=8$, $(x_1,y_1)=(7,4)$, $(x_2,y_2)=(z,-4)$:
$$8=\frac{-4-4}{z-7}$$

Step3: Simplify numerator

Calculate $-4-4=-8$:
$$8=\frac{-8}{z-7}$$

Step4: Solve for $z-7$

Multiply both sides by $z-7$, then divide by 8:
$$z-7=\frac{-8}{8}=-1$$

Step5: Isolate $z$

Add 7 to both sides:
$$z=-1+7$$

Answer:

$6$