Chapter 3.3, Problem 52HP

To determine

Who is correct.

Answer to Problem 52HP

The Luna is correct.

Explanation of Solution

Given information:

Kyle and Luna are finding the value of a so the line passes through the pair of points, $\left(10,a\right)\text{and}\left(-2,8\right)$ and has a slope of $\frac{1}{4}$ .

  

Concept Used:

The slope of a line connecting the points $\left(x_1,y_1\right),\text{ and }\left(x_2,y_2\right)$ is given by the formula

  $\text{Slope }\left(m\right)=\frac{y_2-y_1}{x_2-x_1}$

Calculation:

In order to find the slope of the line passing through the points $\left(10,a\right)\text{and}\left(-2,8\right)$ , use the slope formula and substitute the values $\left(x_1,y_1\right)=\left(10,a\right)\text{and}\left(x_2,y_2\right)=\left(-2,8\right)$ and simplify further as shown below,

  $\begin{array}{c}\text{Slope }\left(m\right)=\frac{y_2-y_1}{x_2-x_1}\\ \frac{1}{4}=\frac{8-a}{-2-10}\\ \frac{1}{4}=\frac{8-a}{-12}\\ \frac{1}{4}\cdot 4=\frac{8-a}{-12}\cdot 4\\ 1=\frac{32-4a}{-12}\\ -12=\frac{32-4a}{-12}\times \left(-12\right)\\ -12=32-4a\\ -12-32=32-4a-32\\ -44=-4a\\ \Rightarrow 4a=44\\ \frac{4a}{4}=\frac{44}{4}\\ a=11\end{array}$

Thus, the Luna is correct.