Chapter 8, Problem 8CT

To determine

To find:

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

Answer to Problem 8CT

x-intercept:

  $(-2,0)$

y-intercept:

  $(0,6)$

Explanation of Solution

Given:

An equation:

  $y=3x+6$

Calculation:

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

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

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:

  $\begin{array}{l}y=3x+6\left(\text{Given equation}\right)\\ y=3(0)+6\left(\text{Substituting }y=0\right)\\ y=0+6\\ y=6\end{array}$

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

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