Chapter 8.4, Problem 29WE

To determine

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

Answer to Problem 29WE

This is the equation of a line making intercept of 0 with y-axis and making angle of ${56.3}^{°}$ anti-clockwise with positive x-axis.

  

Explanation of Solution

Given information:

The equation of line:

  $3x=2y$

Formula used: -

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

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

  $\begin{array}{l}3x=2y\\ \frac{3}{2}x=y\\ y=\frac{3}{2}x\\ y=\frac{3}{2}x+0\end{array}$

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: $c=0$

  $\begin{array}{l}Slope:m=\frac{3}{2}\\ \tan \theta =\frac{3}{2}\\ \theta ={\tan }^{-1}\left(\frac{3}{2}\right)\\ \theta ={56.3}^{°}\end{array}$

So, this is the equation of a line making intercept of 0 with y-axis and making angle of ${56.3}^{°}$ anti-clockwise with positive x-axis.