Q11. - Algebra 2

Question

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

 

$3x+2y=6$

Step-by-Step Solution

Answer

The $x$-intercept is 2 and y-intercept is 3. The graph of the equation is:

Step 1 – Definition of intercepts.

The x-intercept is the point where the graph intersect the x-axis. It is the value of x when y=0.

The y-intercept is the y-intercept is the point where the graph intersect the x-axis. It is the value of y when x=0.

Step 2 – Find the x -intercept.

The given equation is:

$3x+2y=6$

Substitute y=0 in the given equation.

$\begin{array}{c}3x+2\left(0\right)=6\\ 3x+0=6\\ 3x=6\\ \frac{3x}{3}=\frac{6}{3}\\ x=2\end{array}$

The x-intercept is 2. The graph crosses the x-axis at $\left(2,0\right)$.

Step 3 – Find the y -intercept.

Substitute x=0 in the given equation.

$\begin{array}{c}3\left(0\right)+2y=6\\ 0+2y=6\\ 2y=6\\ \frac{2y}{2}=\frac{6}{2}\\ y=3\end{array}$

The y-intercept is 3. The graph crosses the y-axis at $\left(0,3\right)$.

Step 4 – Draw the graph.

Plot the points $\left(2,0\right)$ and $\left(0,3\right)$ on a coordinate plane and connect them by a straight line as shown below:

Thus, the x-intercept is 2 and y-intercept is 3.