directions: find the slope of the line that passes through the given two points. 4. (1, -4) and (-4, -6) 5…

Explanation:

Step1: Recall slope formula

The slope $m$ of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Solve for problem 4

For points $(1,-4)$ and $(-4,-6)$, let $(x_1,y_1)=(1,-4)$ and $(x_2,y_2)=(-4,-6)$. Then $m=\frac{-6-(-4)}{-4 - 1}=\frac{-6 + 4}{-5}=\frac{-2}{-5}=\frac{2}{5}$.

Step3: Solve for problem 5

For points $(-6,2)$ and $(-5,-2)$, let $(x_1,y_1)=(-6,2)$ and $(x_2,y_2)=(-5,-2)$. Then $m=\frac{-2 - 2}{-5-(-6)}=\frac{-4}{-5 + 6}=-4$.

Step4: Solve for problem 6

For points $(-3,3)$ and $(-9,5)$, let $(x_1,y_1)=(-3,3)$ and $(x_2,y_2)=(-9,5)$. Then $m=\frac{5 - 3}{-9-(-3)}=\frac{2}{-9 + 3}=-\frac{1}{3}$.

Step5: Solve for problem 7

For points $(4,-7)$ and $(2,-7)$, let $(x_1,y_1)=(4,-7)$ and $(x_2,y_2)=(2,-7)$. Then $m=\frac{-7-(-7)}{2 - 4}=\frac{-7 + 7}{-2}=0$.

Answer:

4. $\frac{2}{5}$
5. $-4$
6. $-\frac{1}{3}$
7. $0$