Question

Graph each equation.

$2x-3y=6$

Short answer

The required graph is represented by,

Step-by-step solution

Step 1. Determine the x-intercept.

Write x-intercept that can be obtained by using 0 in place of y into the provided equation.

$$\begin{gathered} 2x+3\cdot 0=6 \\ 2x-0=6 \\ 2x=6 \\ \frac{2x}{2}=\frac{6}{2} \\ x=3 \end{gathered}$$

Step 2. Determine the y-intercept.

Write y-intercept that can be obtained by using 0 in place of x into the provided equation.

$$\begin{gathered} 2\cdot 0-3y=6 \\ -3y=6 \\ -\frac{3y}{3}=\frac{6}{3} \\ y=-2 \end{gathered}$$

Step 3. Take the help of x-intercept and y-intercept to draw the required graph.

Graph the points$\left(3,0\right)$ and$\left(0,-2\right)$ generated with the help of x-intercept and y-intercept respectively after it join them with the help of a straight line to get the graphical representation of the provided equation.