Chapter 8.3, Problem 14E

To determine

To find:

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

Answer to Problem 14E

x -intercept: $(6,0)$

y -intercept: $(0,8)$

Explanation of Solution

Given:

An equation: $4x+3y=24$

Calculation:

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

  $\begin{array}{l}4x+3y=24\left(\text{Given equation}\right)\\ 4x+3(0)=24\left(\text{Substituting }y=0\right)\\ 4x=24\\ \frac{4x}{4}=\frac{24}{4}\left(\text{Dividing both sides by 4}\right)\\ x=6\end{array}$

Therefore, the x -intercept of our given equation is $(6,0)$ .

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

  $\begin{array}{l}4x+3y=24\left(\text{Given equation}\right)\\ 4(0)+3y=24\left(\text{Substituting }x=0\right)\\ 3y=24\\ \frac{3y}{3}=\frac{24}{3}\left(\text{Dividing both sides by 3}\right)\\ y=8\end{array}$

Therefore, the y -intercept of our given equation is $(0,8)$ .

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