Chapter 8.3, Problem 12E

To determine

To find:

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

Answer to Problem 12E

x -intercept: $(-2,0)$

y -intercept: $(0,3)$

Explanation of Solution

Given:

An equation: $3x-2y=-6$

Calculation:

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

  $\begin{array}{l}3x-2y=-6\left(\text{Given equation}\right)\\ 3x-2(0)=-6\left(\text{Substituting }y=0\right)\\ 3x=-6\\ \frac{3x}{3}=\frac{-6}{3}\left(\text{Dividing both sides by 3}\right)\\ x=-2\end{array}$

Therefore, the x -intercept of our given equation is $(-2,0)$ .

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

  $\begin{array}{l}3x-2y=-6\left(\text{Given equation}\right)\\ 3(0)-2y=-6\left(\text{Substituting }x=0\right)\\ -2y=-6\\ \frac{-2y}{-2}=\frac{-6}{-2}\left(\text{Dividing both sides by }-2\right)\\ y=3\end{array}$

Therefore, the y -intercept of our given equation is $(0,3)$ .

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