Question

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a line that includes the points (-6, 10) and (-7, z) has a slope of 10. what is the value of z?
z =
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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 $(x_1,y_1)=(-6,10)$, $(x_2,y_2)=(-7,z)$, and $m=10$.
$$10 = \frac{z - 10}{-7 - (-6)}$$
Simplify the denominator: $-7 - (-6) = -7 + 6 = -1$, so:
$$10 = \frac{z - 10}{-1}$$

Step3: Solve for z

Multiply both sides by $-1$:
$$10 \times (-1) = z - 10$$
$$-10 = z - 10$$
Add 10 to both sides:
$$z = -10 + 10$$

Answer:

$0$