Chapter 3.1, Problem 56PPS

To determine

To Graph: The equation $y=\frac{2}{3}x+1$ by using x- and y-intercepts.

Explanation of Solution

Given information:

The given equation $y=\frac{2}{3}x+1$

Calculation:

To find the x-intercept, let $y=0$

  $\begin{array}{l}y=\frac{2}{3}x+1\\ 0=\frac{2}{3}x+1\end{array}$

(Replace y by 0)

  $0-1=\frac{2}{3}x+1-1$

(Subtract -1 on both sides)

  $-1=\frac{2}{3}x$

(Simplify)

  $-1\cdot 3=\frac{2}{3}x\cdot 3$

(Multiply 3 on both sides)

  $-3=2x$

(Simplify)

  $-\frac{3}{2}=\frac{2x}{2}$

(Divide both sides by 2)

  $x=-\frac{3}{2}$

(Simplify)

Or

  $x=-1.5$

The x-intercept is -1.5. This means that the graph intersects the x-axis at $\left(-1.5,0\right)$ .

To find the y-intercept, let $x=0$

  $\begin{array}{l}y=\frac{2}{3}x+1\\ y=\frac{2}{3}\left(0\right)+1\end{array}$

(Replace x by 0)

  $y=1$

(Simplify)

The y-intercept is 1. This means the graph intersects the y-axis at $\left(0,1\right)$ .

Plot these two points and then draw a line through them.