Question

Find the x-intercept and the y-intercept of the graph of each equation. Then graph of the equation.

$2x-6y=12$

Short answer

The x-intercept of the given equation is $6$and the y-intercept is $-2.$

Step-by-step solution

Step 1- Given information

A linear equation $2x-6y=12$.

Step 2- Concept used

The y-coordinate of the point at which a graph crosses the y-axis is called the y-intercept.

So, the y-intercept is the value of $y$whenlocalid="1647007060921" $x=0$

The x-coordinate of the point at which a graph crosses the x-axis is called the x-intercept.

So, the x-intercept is the value of $x$when $y=0.$

Step 3- To find the x-intercept and y-intercept.

From the given information,

$2x-6y=12\left(1\right)$

Substitute the $y=0$in the equation (1).

$\begin{array}{l}2x-6\times 0=12\\ \Rightarrow 2x=12\\ \Rightarrow x=6\end{array}$

Therefore, the x-intercept is $6$and the coordinate is $\left(6,0\right).$

Now, substitute the $x=0$in the given equation (1).

$\begin{array}{l}2\times 0-6y=12\\ \Rightarrow -6y=12\\ \Rightarrow y=-2\end{array}$

Therefore, the y-intercept is $-2$ and coordinate is $\left(0,-2\right).$

Step 4- Graph of the of the given equation

The graph of the given equation is: