Chapter 4.2, Problem 36PPS

To determine

The equation of line with coordinates (-4, 8) and (3, -7).

Answer to Problem 36PPS

The equation of line is $7y+15x=-4$ .

Explanation of Solution

Given:

The line has coordinates (-4, 8) and (3, -7).

Calculation:

Standard equation of slope intercept form is expressed as follows:

$y=mx+c$

Here, m is slope and c stands for constant.

Following are the steps to determine the equation of line:

Step1:

Determine the slope of the line.

$\begin{array}{c}m=\frac{y_2-y_1}{x_2-x_1}\\ =\frac{-7-8}{3-\left(-4\right)}\\ =-\frac{15}{7}\end{array}$

Step2:

Substitute the slope in the slope intercept form as follows:

$y=-\frac{15}{7}x+c$

Step3:

Substitute the (-4, 8) in above equation as follows:

  $\begin{array}{l}8=-\frac{15}{7}\left(-4\right)+c\\ c=8-\frac{60}{7}\\ c=-\frac{4}{7}\end{array}$

Thus, the equation of line is calculated as follows:

$\begin{array}{l}y=-\frac{15}{7}x-\frac{4}{7}\\ 7y+15x=-4\end{array}$

Thus, the equation of line is $7y+15x=-4$ .