Chapter 3.1, Problem 4AGP

To determine

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

Answer to Problem 4AGP

The required answer is:

  

Explanation of Solution

Given information:

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

Calculation:

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

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

(Replace y by 0)

  $-x=3$

(Simplify)

  $-x\left(-1\right)=3\left(-1\right)$

(Multiply by -1 on both sides)

  $x=-3$

(Simplify)

The x-intercept is -3. This means that the graph intersects the x-axis at $\left(-3,0\right)$ .

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

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

(Replace x by 0)

  $2y=3$

(Simplify)

  $\frac{2y}{2}=\frac{3}{2}$

(Divide both sides by 2)

  $y=\frac{3}{2}$

(Simplify)

Or

  $y=1.5$

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

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