Given the word problem, we can deduce the following information:
1. Points (2,a) and (-4,-10).
2. Slope = 8
To determine the value of a, we use the formula:
[tex]\text{slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
Based on the given values, we let:
[tex]\begin{gathered} x_1=2 \\ y_1=a \\ x_2=-4 \\ y_2=-10 \end{gathered}[/tex]
We plug in what we know:
[tex]\begin{gathered} \text{slope}=\frac{y_2-y_1}{x_2-x_1} \\ 8=\frac{-10-a}{-4-2} \\ \text{Simplify and rearrange} \\ 8=\frac{-10-a}{-6} \\ 8(-6)=-10-a \\ -48=-10-a \\ a=-10+48 \\ \text{Calculate} \\ a=38 \end{gathered}[/tex]
Therefore, the value of a is 38.
