Question

Find the x-intercept and y-intercept of the graph of each linear function.

Short answer

The x-intercept is$x=-8$ and the y-intercept is $y=6$.

Step-by-step solution

Step 1. Find the slope of the line.

Find the equation of the line using any two points. Use the formula to find slope of the line:

$$\begin{gathered} m=\frac{y_2-y_1}{x_2-x_1} \\ m=\frac{3-0}{-4-\left(-8\right)} \\ m=\frac{3}{-4+8} \\ m=\frac{3}{4} \end{gathered}$$

Step 2. Find the equation of the line.

The equation of a line is given by,

$$\begin{gathered} y-y_1=m\left(x-x_1\right) \\ y-0=\frac{3}{4}\left(x-\left(-8\right)\right) \\ 4y=3\left(x+8\right) \\ 4y=3x+24 \end{gathered}$$

Step 3. Find the x and y intercepts.

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

$$\begin{gathered} 4y=3x+24 \\ 4\left(0\right)=3x+24\text{[Plugin}y=0] \\ 0=3x+24 \\ 3x=-24 \\ x=-8 \end{gathered}$$

x-Intercept: $x=-8$.

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

$$\begin{gathered} 4y=3x+24 \\ 4y=3\left(0\right)+24\text{[Plugin}x=0] \\ 4y=0+24 \\ 4y=24 \\ y=6 \end{gathered}$$

y-Intercept: $y=6$.