Question

homework 1: slopes of parallel & perpendicular lines

1. find slope for each of the following graphs.

Explanation:

Step1: Recall slope - formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.

Step2: For the first graph

Let's take two points, say $(0,0)$ and $(1,1)$. Then $m=\frac{1 - 0}{1 - 0}=1$.

Step3: For the second graph

Take two points, for example, $(0,1)$ and $(1,0)$. Then $m=\frac{0 - 1}{1 - 0}=- 1$.

Step4: For the third graph

The line is horizontal. For any two points $(x_1,y)$ and $(x_2,y)$ on a horizontal line, $m=\frac{y - y}{x_2 - x_1}=0$.

Answer:

The slopes of the three lines are 1, - 1, and 0 respectively.