Question

slope=
slope=
is the slope the same in each? why?
lesson 2: rsg

Explanation:

Step1: Recall slope - formula

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Identify two points on the line

Let's take two points on the line. For example, in the first graph, if we take the points $(2, - 2)$ and $(4,-4)$.

Step3: Calculate the slope

$m=\frac{-4-(-2)}{4 - 2}=\frac{-4 + 2}{2}=\frac{-2}{2}=-1$.

Step4: Check for the second graph

In the second graph, using the same - looking points (since the lines are the same), say $(2,-2)$ and $(4,-4)$, $m=\frac{-4-(-2)}{4 - 2}=\frac{-2}{2}=-1$.

Answer:

The slope of each line is - 1. The slopes are the same because they are the same line (or parallel lines with the same steepness in this case, and for a straight - line, the slope is constant everywhere on the line). The slope is calculated as $\frac{\text{change in }y}{\text{change in }x}$, and for both sets of points on the two lines (which are essentially the same line), the ratio of the vertical change to the horizontal change is the same.