Question

Solve each equation by graphing

$12x=4x+16$

Short answer

The x and y intercepts by using graphing are$x=2$ and $y=0$.

Step-by-step solution

Step 1. State the concept for plotting a straight line using equation.

The x-intercepts are where the graph crosses the x-axis, and the y-intercepts are where the graph crosses the y-axis.

Then, algebraically,

• an x-intercept is a point on the graph where y is zero, and
• a y-intercept is a point on the graph where x is zero.

More specifically,

• an x-intercept is a point in the equation where the y-value is zero, and
• a y-intercept is a point in the equation where the x-value is zero.

Step 2. Find the intercepts.

Graph the equation by using x and y-intercept method. First, find the x and y intercept from the equation and then plot the points on the grid and join then to complete the graph.

Find the x-intercept, plug in $y=0$in the equation.

$$\begin{gathered} 12x=4x+16 \\ 12x-4x=4x+16-4x\text{[Plugin}y=0] \\ 8x=16 \\ \frac{8x}{8}=\frac{16}{8} \\ x=2 \end{gathered}$$

x-Intercept: $x=2$

Find the y-intercept, plug in $x=2$in the equation.

$$\begin{gathered} 12x=4x+16 \\ 12\left(0\right)=4\left(0\right)\text{+16[Plugin}x=0] \\ 0 \\ y=0\text{[Sinceno}y\text{isintheequation}] \end{gathered}$$

y-Intercept:$y=0$

Step 3. Plot the graph.

Graph the line $12x=4x+16$with x and y intercepts points are$\left(2,0\right)$ and $\left(0,0\right)$.

Thus, x and y intercepts are $x=2$and $y=0$.