Chapter 3.1, Problem 53PPS

To determine

To Graph: The equation $2x-3y=5$ by using x- and y-intercepts.

Explanation of Solution

Given information:

The given equation $2x-3y=5$

Calculation:

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

  $\begin{array}{l}2x-3y=5\\ 2x-3\left(0\right)=5\end{array}$

(Replace y by 0)

  $2x=5$

(Simplify)

  $\frac{2x}{2}=\frac{5}{2}$

(Divide both sides by 2)

  $x=\frac{5}{2}$

(Simplify)

Or

  $x=2.5$

The x-intercept is 2.5. This means that the graph intersects the x-axis at $\left(2.5,0\right)$ .

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

  $\begin{array}{l}2x-3y=5\\ 2\left(0\right)-3y=5\end{array}$

(Replace x by 0)

  $-3y=5$

(Simplify)

  $-\frac{3y}{3}=\frac{5}{3}$

(Divide both sides by 3)

  $-y=\frac{5}{3}$

(Simplify)

  $-y\left(-1\right)=\frac{5}{3}\left(-1\right)$

(Multiply -1 on both sides)

  $y=-\frac{5}{3}$

(Simplify)

Or

  $y=-1.66$

The y-intercept is -1.66. This means the graph intersects the y-axis at $\left(0,-1.66\right)$ .

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