Question

Graph each equation by using the $x$- and $y$-intercepts.

$-x+2y=3$

Short answer

The graph of the equation$-x+2y=3$is:

Step-by-step solution

Step 1. Find the x and y- intercepts of the equation −x+2y=3.

To find the $x$-intercept, substitute 0 for$y$ and find the value of $x$.

role="math" localid="1647329138275" $$\begin{gathered} -x+2y=3 \\ -x+2\left(0\right)=3 \\ -x+0=3 \\ -x=3 \\ x=-3 \end{gathered}$$

Therefore, the $x$-intercept is $-3$.

As, the $x$-intercept is$-3$ that means the graph of$-x+2y=3$ will intersect the $x$-axis at $\left(-3,0\right)$.

To find the $y$-intercept, substitute 0 for$x$ and find the value of $y$.

role="math" localid="1647329287395" $\begin{array}{c}-x+2y=3\\ -0+2y=3\\ 2y=3\\ y=\frac{3}{2}\end{array}$

Therefore, the $y$-intercept is $\frac{3}{2}$.

As, the $y$-intercept is$\frac{3}{2}$ that means the graph of$-x+2y=3$ will intersect the $y$-axis at $\left(0,\frac{3}{2}\right)$.

Step 2. Draw the graph of the equation −x+2y=3.

Draw the graph of$-x+2y=3$ the equation by using the information that the graph of the equation$-x+2y=3$ is a line passing through the points$\left(-3,0\right)$ and $\left(0,\frac{3}{2}\right)$.

Therefore, the graph of the equation$-x+2y=3$ is: