Chapter 8.3, Problem 17E

To determine

To find:

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

Answer to Problem 17E

x -intercept: $(7,0)$

y -intercept: $(0,7)$

Explanation of Solution

Given:

An equation: $y=-x+7$

Calculation:

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

  $\begin{array}{l}y=-x+7\left(\text{Given equation}\right)\\ 0=-x+7\left(\text{Substituting }y=0\right)\\ 0-7=-x+7-7\left(\text{Subtracting 7 from both sides}\right)\\ -7=-x\\ -x=-7\\ \frac{-x}{-1}=\frac{-7}{-1}\left(\text{Dividing both sides by }-1\right)\\ x=7\end{array}$

Therefore, the x -intercept of our given equation is $(7,0)$ .

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

  $\begin{array}{l}y=-x+7\left(\text{Given equation}\right)\\ y=-0+7\left(\text{Substituting }x=0\right)\\ y=7\end{array}$

Therefore, the y -intercept of our given equation is $(0,7)$ .

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