Question

1. what is the slope of the line that passes through the points $(4, 7)$ and $(7, 16)$? write your answer in simplest form.
2. what is the slope of the line that passes through the points $(1, -9)$ and $(4, -7)$? write your answer in simplest form.

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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For Question 4:

Step2: Assign values to variables

Let $(x_1,y_1)=(4,7)$ and $(x_2,y_2)=(7,16)$.

Step3: Calculate slope

$m=\frac{16-7}{7-4}=\frac{9}{3}=3$
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For Question 5:

Step2: Assign values to variables

Let $(x_1,y_1)=(1,-9)$ and $(x_2,y_2)=(4,-7)$.

Step3: Calculate slope

$m=\frac{-7-(-9)}{4-1}=\frac{-7+9}{3}=\frac{2}{3}$

Answer:

1. For the line through $(4,7)$ and $(7,16)$: $3$
2. For the line through $(1,-9)$ and $(4,-7)$: $\frac{2}{3}$