Chapter 8.5, Problem 24WE

To determine

To find: The equation in slope intercept form of the given line.

Answer to Problem 24WE

The equation in slope intercept form of the given lineis $y=-\frac{5}{4}x-\frac{17}{4}$ .

Explanation of Solution

Given information:

The points through the line passes is $\left(-3,-1\right),\left(1,-4\right)$ .

Calculation:

The slope of the line is,

  $\begin{array}{c}m=\frac{y_2-y_2}{x_2-x_1}\\ =\frac{-4-1}{1+3}\\ =\frac{-5}{4}\end{array}$

The slope intercept form is,

  $y=mx+c$

Here, the slope is $m$ and $y$ intercept is $c$ .

Substitute the values in above equation.

  $y=-\frac{5}{4}x+c$ .................(1)

Substitute the values of point through which the line is passing in above equation.

  $\begin{array}{c}-3=-\frac{5}{4}\left(-1\right)+c\\ -3=\frac{5}{4}+c\\ c=-\frac{17}{4}\end{array}$

Substitute the value in equation (1).

  $y=-\frac{5}{4}x-\frac{17}{4}$