Q12. - Algebra 2

Question

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

 

$4x+8y=12$

Step-by-Step Solution

Answer

The x-intercept is 3 and y-intercept is 1.5. 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:

$4x+8y=12$

Substitute y=0 in the given equation.

$\begin{array}{c}4x+8\left(0\right)=12\\ 4x+0=12\\ 4x=12\\ \frac{4x}{4}=\frac{12}{4}\\ x=3\end{array}$

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

Step 3 – Find the y -intercept.

Substitute x=0 in the given equation.

$\begin{array}{c}4\left(0\right)+8y=12\\ 0+8y=12\\ 8y=12\\ \frac{8y}{8}=\frac{12}{8}\\ y=1.5\end{array}$

The y-intercept is 1.5. The graph crosses the y-axis at $\left(0,1.5\right)$.

Step 4 – Draw the graph.

Plot the points $\left(3,0\right)$ and $\left(0,1.5\right)$ on a coordinate plane and connect them by a straight line as shown below:

Thus, the x-intercept is 3 and y-intercept is 1.5.