Answer:
[tex]2[/tex] would be the slope of a line that goes between [tex](-4,\, -8)[/tex] and [tex](3,\, 6)[/tex].
Step-by-step explanation:
Given a line that goes through two points, [tex](x_{0},\, y_{0})[/tex] and [tex](x_{1},\, y_{1})[/tex] ([tex]x_{0} \ne x_{1}[/tex],) the slope of this line would be equal to the "rise over run" between these two points.
"Rise" refers to the change in the [tex]y[/tex]-coordinate between the two points, [tex](y_{1} - y_{0})[/tex]. Similarly, "run" refers to the change in the [tex]x[/tex]-coordinate, [tex](x_{1} - x_{0})[/tex].
[tex]\begin{aligned} \text{slope} &= \frac{\text{rise}}{\text{run}} \\ &= \frac{y_{1} - y_{0}}{x_{1} - x_{0}}\end{aligned}[/tex].
For [tex](-4,\, -8)[/tex], the [tex]x[/tex]-coordinate is [tex]x_{0} = (-4)[/tex] and the [tex]y[/tex]-coordinate is [tex]y_{0} = -8[/tex].
For [tex](3,\, 6)[/tex], the [tex]x[/tex]-coordinate is [tex]x_{1} = 3[/tex] and the [tex]y[/tex]-coordinate is [tex]y_{1} = 6[/tex].
The "rise" between these two points would be [tex]y_{1} - y_{0} = 6 - (-8) = 14[/tex].
The "run" between these two points would be [tex]x_{1} - x_{0} = 3 - (-4) = 7[/tex].
Thus, the slope of a line that goes through the two points would be:
[tex]\begin{aligned} \text{slope} &= \frac{\text{rise}}{\text{run}} \\ &= \frac{y_{1} - y_{0}}{x_{1} - x_{0}} \\ &= \frac{14}{7} \\ &= 2\end{aligned}[/tex].
