Q4A. - Algebra 1

Question

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

$-x+2y=3$

Step-by-Step Solution

Answer

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

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

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

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

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 $y$.

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

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 + 2 y = 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: