Question

I need help with this problem. The points (2,a) and (-4,-10) fall on a line with a slope of 8. What is the value of a?

Answer 1

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:

`\text{slope}=(y_2-y_1)/(x_2-x_1)`

Based on the given values, we let:

`\begin{gathered} x_1=2 \\ y_1=a \\ x_2=-4 \\ y_2=-10 \end{gathered}`

We plug in what we know:

`\begin{gathered} \text{slope}=(y_2-y_1)/(x_2-x_1) \\ 8=(-10-a)/(-4-2) \\ \text{Simplify and rearrange} \\ 8=(-10-a)/(-6) \\ 8(-6)=-10-a \\ -48=-10-a \\ a=-10+48 \\ \text{Calculate} \\ a=38 \end{gathered}`

Therefore, the value of a is 38.