Certainly! To determine the slope [tex]\( m \)[/tex] between the given points [tex]\((2, 5)\)[/tex] and [tex]\((4, 13)\)[/tex], we can use the slope formula:
[tex]\[
m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}
\][/tex]
Here are the coordinates of the two points:
- [tex]\( (x_1, y_1) = (2, 5) \)[/tex]
- [tex]\( (x_2, y_2) = (4, 13) \)[/tex]
We can substitute these values into the formula:
1. Calculate the rise:
[tex]\[ y_2 - y_1 = 13 - 5 = 8 \][/tex]
2. Calculate the run:
[tex]\[ x_2 - x_1 = 4 - 2 = 2 \][/tex]
3. Calculate the slope (m) by dividing the rise by the run:
[tex]\[
m = \frac{\text{rise}}{\text{run}} = \frac{8}{2} = 4.0
\][/tex]
So, the slope [tex]\( m \)[/tex] between the points [tex]\( (2, 5) \)[/tex] and [tex]\( (4, 13) \)[/tex] is [tex]\( 4.0 \)[/tex]. Thus, the step-by-step solution includes finding that the rise is [tex]\( 8 \)[/tex] and the run is [tex]\( 2 \)[/tex], which gives us a slope of [tex]\( 4.0 \)[/tex].
