Chapter 8.3, Problem 13E

To determine

To find:

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

Answer to Problem 13E

x -intercept: $(-5,0)$

y -intercept: $(0,-4)$

Explanation of Solution

Given:

An equation: $4x+5y=-20$

Calculation:

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

  $\begin{array}{l}4x+5y=-20\left(\text{Given equation}\right)\\ 4x+5(0)=-20\left(\text{Substituting }y=0\right)\\ 4x=-20\\ \frac{4x}{4}=-\frac{20}{4}\left(\text{Dividing both sides by 4}\right)\\ x=-5\end{array}$

Therefore, the x -intercept of our given equation is $(-5,0)$ .

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

  $\begin{array}{l}4x+5y=-20\left(\text{Given equation}\right)\\ 4(0)+5y=-20\left(\text{Substituting }x=0\right)\\ 5y=-20\\ \frac{5y}{5}=-\frac{20}{5}\left(\text{Dividing both sides by 5}\right)\\ y=-4\end{array}$

Therefore, the y -intercept of our given equation is $(0,-4)$ .

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