Chapter 8, Problem 4CST

To determine

What is the slope of the line with equation $-x+4y=-24$ ?

Answer to Problem 4CST

The slope of the line with equation $-x+4y=-24$ is $\frac{1}{4}$ and option G is the correct choice.

Explanation of Solution

Given:

Four choices:

  $\text{F}\text{. }-6\text{ G}\text{. }\frac{1}{4}\text{ H}\text{. }6\text{ I}\text{. }24$

Concept used:

We know that slope-intercept form of equation is in format: $y=mx+b,\text{where,}$

  $\begin{array}{l}m=\text{Slope of line,}\\ b=\text{The }y\text{-intercept}\end{array}$

Calculation:

First of all, we will convert our given equation in slope-intercept form as shown below:

  $\begin{array}{l}-x+4y=-24\left(\text{Given equation}\right)\\ -x+x+4y=-24+x\left(\text{Adding }x\text{}\text{ on both sides}\right)\\ 4y=x-24\\ \frac{4y}{4}=\frac{x}{4}-\frac{24}{4}\left(\text{Dividing both sides by 4}\right)\\ y=\frac{1}{4}x-6\end{array}$

Upon looking at our equation, we can see that the value of m is $\frac{1}{4}$ .

Therefore, the slope of the line with equation $-x+4y=-24$ is $\frac{1}{4}$ and option G is the correct choice.