Chapter 1.3, Problem 20E

To determine

To graph: the equation, $y=\frac{2}{3}x-4$

Answer to Problem 20E

  

Explanation of Solution

Given information: $y=\frac{2}{3}x-4$

Calculation:

The above equation is already in slope intercept form. Now find value of y , by substituting different value of x.

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

  $\begin{array}{c}y=\frac{2}{3}x-4\\ =\frac{2}{3}\left(2\right)-4\\ =\frac{4}{3}-4\\ =\frac{4-12}{3}\\ =-\frac{8}{3}\end{array}$

So, the first coordinate is $\left(2,-\frac{8}{3}\right)$ .

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

  $\begin{array}{c}y=\frac{2}{3}x-4\\ =\frac{2}{3}\left(-2\right)-4\\ =\frac{-4}{3}-4\\ =\frac{-4-12}{3}\\ =-\frac{16}{3}\end{array}$

So, the second coordinate is $\left(-2,-\frac{16}{3}\right)$ .

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