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.

$$\begin{gathered} 5x+2\cdot 0=10 \\ 5x+0=10 \\ 5x=10 \\ \frac{5x}{5}=\frac{10}{5} \\ x=2 \end{gathered}$$

Step 2. Determine the y-intercept.

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

$$\begin{gathered} 5\left(0\right)+2y=10 \\ 2y=10 \\ \frac{2y}{2}=\frac{10}{2} \\ y=5 \end{gathered}$$

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

Graph the points$\left(2,0\right)$ and$\left(0,5\right)$ 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.