Chapter 8.4, Problem 18WE

To determine

To Find: Plot the graph of given equation using slope and y-intercept.

Answer to Problem 18WE

This is the equation of a line making intercept of 3 with negative y-axis and making angle of ${38.6}^{°}$ clockwise with positive x-axis.

  

Explanation of Solution

Given information:

The equation of line:

  $y=-\frac{3}{4}x-5$

Formula used: -

Slope form of line: $y=mx+c$ .

Where $m$ is the slope of line, and $c$ is the $y$ -intercept when $x=0$ .

  $y=-\frac{3}{4}x+\left(-5\right)$

Recall that Slope form of line: $y=mx+c$ .

Where $m$ is the slope of line, and $c$ is the $y$ -intercept when $x=0$ .

By comparing equations, we get

y-intercept: $c=-5$

  $\begin{array}{l}Slope:m=-\frac{3}{4}\\ \tan \theta =-\frac{3}{4}\\ \theta ={\tan }^{-1}\left(-\frac{3}{4}\right)\\ \theta =-{36.8}^{°}\end{array}$

So, this is the equation of a line making intercept of 5 with negative y-axis and making angle of ${36.8}^{°}$ clockwise with positive x-axis.