Chapter 8, Problem 3CST

To determine

What is the y-intercept of the graph of $-x+4y=-24$ ?

Answer to Problem 3CST

The y-intercept of the graph of $-x+4y=-24$ is $-6$ and option A is the correct choice.

Explanation of Solution

Given:

Four choices:

  $\text{A}\text{. }-6\text{ B}\text{. }4\text{ C}\text{. }6\text{ D}\text{. }24$

Calculation:

To find, the y-intercept of our given equation, we will substitute $x=4$ in our given equation and solve for y as:

  $\begin{array}{l}-x+4y=-24\left(\text{Given equation}\right)\\ -0+4y=-24\left(\text{Substituting }x=0\right)\\ 4y=-24\\ \frac{4y}{4}=-\frac{24}{4}\\ y=-6\end{array}$

Therefore, the y-intercept of the graph of our given equation is $-6$ and option A is the correct choice.