Chapter 13.2, Problem 24WE

To determine

To find unknown $x$ -coordinate of one of point given.

Answer to Problem 24WE

The unknown $x$ -coordinate is

  $x_2=3$

Explanation of Solution

Given:

A line with slope $-\frac{5}{2}$ passes through points $\left(7,-4\right)\text{ and }\left(?,6\right)$

Calculation:

Slope of a line when two points $\left(x_1,y_1\right)$ and $\left(x_2,y_2\right)$ are given is

  $m=\frac{y_2-y_1}{x_2-x_1}$

Points given are $\left(7,-4\right)\text{ and }\left(?,6\right)$

Let the unknown $x$ -coordinate be $x_2$

So,

  $\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ -\frac{5}{2}=\frac{6-\left(-4\right)}{x_2-7}\\ -\frac{5}{2}=\frac{10}{x_2-7}\\ -5\left(x_2-7\right)=20\\ -5x_2+35=20\\ -5x_2=-15\\ x_2=3\end{array}$

So, the unknown $x$ -coordinate is

  $x_2=3$