Question

1. find the slope of the lines below.

a) $m =$
b) $m =$
c) $m =$
d) $m =$
e) $m =$
f) $m =$
g) $m =$
h) $m =$

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 also find the slope by counting the rise (vertical change) over the run (horizontal change) on the graph.

Step2: Analyze graph a

Pick two points on the line in graph a, say $(0, - 1)$ and $(2,0)$. Then $m=\frac{0-( - 1)}{2 - 0}=\frac{1}{2}$.

Step3: Analyze graph b

Pick two points, e.g., $(0,2)$ and $(2,0)$. Then $m=\frac{0 - 2}{2-0}=-1$.

Step4: Analyze graph c

Pick two points like $(0,-2)$ and $(1,0)$. Then $m=\frac{0-( - 2)}{1 - 0}=2$.

Step5: Analyze graph d

Pick two points such as $(0,1)$ and $(2,-1)$. Then $m=\frac{-1 - 1}{2-0}=-1$.

Step6: Analyze graph e

The line is vertical. For a vertical line, the denominator in the slope - formula $x_2 - x_1 = 0$. So the slope is undefined.

Step7: Analyze graph f

Pick two points, e.g., $(0,2)$ and $(2,0)$. Then $m=\frac{0 - 2}{2-0}=-1$.

Step8: Analyze graph g

Pick two points like $(0,-2)$ and $(2,0)$. Then $m=\frac{0-( - 2)}{2 - 0}=1$.

Step9: Analyze graph h

The line is horizontal. For a horizontal line, $y_2 - y_1=0$. So $m = 0$.

Answer:

a) $m=\frac{1}{2}$
b) $m=-1$
c) $m = 2$
d) $m=-1$
e) Undefined
f) $m=-1$
g) $m = 1$
h) $m = 0$