Chapter 8, Problem 8MCQ

To determine

To find:

The intercepts of theequation’s graph. Then graph the equation.

Answer to Problem 8MCQ

The x-intercept of our given equation would be $2$ .

The y-intercept of our given equation would be $-8$ .

Explanation of Solution

Given:

An equation:

  $4x-y=8$

Calculation:

To find x-intercept, we will substitute $y=0$ in our given equation and solve for x as shown below:

  $\begin{array}{l}4x-y=8\left(\text{Given equation}\right)\\ 4x-0=8\left(\text{Substituting }y=0\right)\\ 4x=8\\ \frac{4x}{4}=\frac{8}{4}\left(\text{Dividing both sides by 4}\right)\\ x=2\end{array}$

Therefore, the x-intercept of our given equation is $2$ .

To find y-intercept, we will substitute $x=0$ in our given equation and solve for y as shown below:

  $\begin{array}{l}4x-y=8\left(\text{Given equation}\right)\\ 4(0)-y=8\left(\text{Substituting }x=0\right)\\ -y=8\\ \frac{-y}{-1}=\frac{8}{-1}\left(\text{Dividing both sides by }-\text{1}\right)\\ y=-8\end{array}$

Therefore, the y-intercept of our given equation is $-8$ .

Upon graphing our given equation, we will get our required graph as shown below: