Q.3.16 - Intermediate Algebra

Question

Find the intercepts:

$x+4y=8$

Step-by-Step Solution

Answer

The intercepts are the points $\left(8,0\right),\left(0,2\right)$

Step 1. Given Information

The given equation is $x+4y=8$

The intercepts of the equation are to be determined.

Step 2. Find the x-intercept

To determine the x-intercept, plugging $y=0$ in the equation and solving for x:

$$\begin{gathered} x+4y=8 \\ x+4\left(0\right)=8 \\ x+0=8 \\ x=8 \end{gathered}$$

So the x intercept is $\left(8,0\right)$

Step 3. Find the y-intercept

To determine the y-intercept, plugging $x=0$ in the equation and solving for y:

$$\begin{gathered} x+4y=8 \\ 0+4y=8 \\ 4y=8 \\ \frac{4y}{4}=\frac{8}{4} \\ y=2 \end{gathered}$$

So the y intercept is $\left(0,2\right)$

Step 4. Conclusion

The intercepts of the equation are the point $\left(8,0\right),\left(0,2\right)$