Chapter 1.4, Problem 18E

To determine

To find: line equation in slope-intercept form.

Answer to Problem 18E

  $y=\frac{5}{8}x+5$

Explanation of Solution

Given information:

  $\begin{array}{l}x\text{-intercept}=-8\\ y\text{-intercept}=5\end{array}$

The coordinates $\left(x_1,y_1\right)$ on x-intercept = $\left(-8,0\right)$

The coordinates $\left(x_2,y_2\right)$ on y-intercept = $\left(0,5\right)$

Calculation

The point slope form is as follows:

  $y-y_1=m\left(x-x_1\right)$ … (1)

The equation slope is as follows:

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

Substitute the value of m in equation (1) to get,

  $y-y_1=\frac{\left(y_2-y_1\right)}{\left(x_2-x_1\right)}\left(x-x_1\right)$ … (2)

Substitute the given points in equation (2) and simply it as follows:

  $\begin{array}{c}y-0=\frac{\left(5-0\right)}{\left(0-\left(-8\right)\right)}\left(x-\left(-8\right)\right)\\ y=\frac{5}{8}\left(x+8\right)\\ y=\frac{5}{8}x+\frac{5}{8}\left(8\right)\\ y=\frac{5}{8}x+5\end{array}$

The slope intercept form is of the line is $y=\frac{5}{8}x+5$ .