Question

fill in the blanks below.
(a) find the slope of the line passing through the points $(-3, 7)$ and $(-3, -6)$.
slope:
(b) find the slope of the line passing through the points $(-4, -2)$ and $(9, -2)$.
slope:

Explanation:

Step1: Recall slope formula

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

Step2: Substitute points (-3,7), (-3,-6)

$m=\frac{-6-7}{-3-(-3)}=\frac{-13}{0}$

Step3: Evaluate undefined slope

Division by 0 is undefined, so the slope is undefined.
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Part (b)

Step4: Substitute points (-4,-2), (9,-2)

$m=\frac{-2-(-2)}{9-(-4)}=\frac{0}{13}$

Step5: Simplify the fraction

$\frac{0}{13}=0$

Answer:

(a) undefined
(b) 0