Certainly! Let's go through the problem step-by-step.
1. Identify the coordinates of the points:
- Point 1: \((-2, -5)\)
- Point 2: \((2, 3)\)
2. Calculate the rise (change in y):
[tex]\[
\text{Rise} = y_2 - y_1
\][/tex]
Substituting the given values:
[tex]\[
\text{Rise} = 3 - (-5) = 3 + 5 = 8
\][/tex]
3. Calculate the run (change in x):
[tex]\[
\text{Run} = x_2 - x_1
\][/tex]
Substituting the given values:
[tex]\[
\text{Run} = 2 - (-2) = 2 + 2 = 4
\][/tex]
4. Calculate the slope using rise over run:
[tex]\[
\text{Slope} = \frac{\text{Rise}}{\text{Run}}
\][/tex]
Substituting the calculated values:
[tex]\[
\text{Slope} = \frac{8}{4} = 2.0
\][/tex]
So, the rise is 8, the run is 4, and the slope of the line passing through the points [tex]\((-2, -5)\)[/tex] and [tex]\((2, 3)\)[/tex] is [tex]\(2.0\)[/tex].
