Chapter 13, Problem 13RP

To determine

To find: The x intercept of the line for the given points.

Answer to Problem 13RP

The x intercept is $\frac{-29}{4}$ .

Explanation of Solution

Given:

The given points are $\left(-2,3\right)$ and $\left(5,7\right)$ .

Calculation:

The formula to determine the slope of the line is of the form,

  $m=\frac{y_2-y_1}{x_2-x_1}$

Then, from the Figure 1 the slope of the points between the two points $\left(-2,3\right),\left(5,7\right)$ is,

  $\begin{array}{l}\frac{y-3}{x-\left(-2\right)}=\frac{7-3}{5-\left(-2\right)}\\ \frac{y-3}{x+2}=\frac{4}{7}\end{array}$

The equation of the line is of the form as,

  $y_2-y_1=m\left(x_2-x_1\right)$

Then,

  $\begin{array}{l}0-3=\frac{4}{7}\left(x+2\right)\\ x=\frac{-29}{4}\end{array}$