Question

for problems 2 - 7, find the slope of the line.

Explanation:

Step1: Recall slope formula

The slope formula for a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. We can pick two distinct integer - valued points on each line from the graph.

Step2: For problem 2

Pick two points, say $(- 10,0)$ and $(0,6)$. Then $x_1=-10,y_1 = 0,x_2 = 0,y_2=6$. Substitute into the slope formula: $m=\frac{6 - 0}{0-(-10)}=\frac{6}{10}=\frac{3}{5}$.

Step3: For problem 3

Pick two points, say $(-10,-6)$ and $(10,-5)$. Then $x_1=-10,y_1=-6,x_2 = 10,y_2=-5$. Substitute into the slope formula: $m=\frac{-5-(-6)}{10 - (-10)}=\frac{-5 + 6}{10+10}=\frac{1}{20}$.

Step4: For problem 4

Pick two points, say $(0,-9)$ and $(2,1)$. Then $x_1 = 0,y_1=-9,x_2=2,y_2 = 1$. Substitute into the slope formula: $m=\frac{1-(-9)}{2 - 0}=\frac{1 + 9}{2}=\frac{10}{2}=5$.

Step5: For problem 5

Pick two points, say $(-10,0)$ and $(0,8)$. Then $x_1=-10,y_1 = 0,x_2 = 0,y_2=8$. Substitute into the slope formula: $m=\frac{8 - 0}{0-(-10)}=\frac{8}{10}=\frac{4}{5}$.

Answer:

Problem 2: $\frac{3}{5}$
Problem 3: $\frac{1}{20}$
Problem 4: $5$
Problem 5: $\frac{4}{5}$