Chapter 1.3, Problem 14E

To determine

To graph: the equation, $2x-3y+15=0$

Answer to Problem 14E

  

Explanation of Solution

Given information: $2x-3y+15=0$

Calculation:

The above equation can be rewritten in slope intercept formula as follows:

  $\begin{array}{c}2x-3y+15=0\\ 3y=2x+15\\ y=\frac{2}{3}x+5\left(\text{Slope intercept form}\right)\end{array}$

Now find value of y ,by substituting different value of x.

Put $x=2$ in the slope intercept equation and simplify it as follows:

  $\begin{array}{c}y=\frac{2}{3}x+5\\ y=\frac{2}{3}\left(2\right)+5\\ =\frac{4}{3}+5\\ =\frac{19}{3}\end{array}$

So, the first coordinate is $\left(2,\frac{19}{3}\right)$ .

Put $x=-2$ in the slope intercept equation and simplify it as follows:

  $\begin{array}{c}y=\frac{2}{3}x+5\\ y=\frac{2}{3}\left(-2\right)+5\\ =\frac{-4}{3}+5\\ =\frac{11}{3}\end{array}$

So, the second coordinate is $\left(-2,\frac{11}{3}\right)$ .

Now, graph the line straight to these points, and it will be formed as follows: