Question

now write the slope of the line of reflection and any dotted line. slope of one of the dotted lines: $\frac{1}{2}$ slope of the line of reflection: $\frac{1}{2}$

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: Identify points on the line of reflection

For the line of reflection, we can choose two points, say $(- 8,0)$ and $(-2,3)$.

Step3: Calculate the slope of the line of reflection

$m=\frac{3 - 0}{-2-(-8)}=\frac{3}{6}=\frac{1}{2}$.

Step4: Identify points on a dotted line

For a dotted line, we can also choose two points. Let's assume two points on a dotted line are such that the vertical change (rise) and horizontal change (run) give the same ratio as the line of reflection. Since the dotted lines are related to the reflection and have the same steepness, their slope is also calculated in the same way. If we take appropriate points on a dotted line, using the slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$, we get $m=\frac{1}{2}$.

Answer:

Slope of one of the dotted lines: $\frac{1}{2}$
Slope of the line of reflection: $\frac{1}{2}$