Chapter 8.3, Problem 26E

To determine

To find:

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

Answer to Problem 26E

x -intercept: $(1.5,0)$

y -intercept: $(0,-3.5)$

Explanation of Solution

Given:

An equation: $y=\frac{7}{3}x-\frac{7}{2}$

Calculation:

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

  $\begin{array}{l}y=\frac{7}{3}x-\frac{7}{2}\left(\text{Given equation}\right)\\ 0=\frac{7}{3}x-\frac{7}{2}\left(\text{Substituting }y=0\right)\\ 0+\frac{7}{2}=\frac{7}{3}x-\frac{7}{2}+\frac{7}{2}\left(\text{Adding }\frac{7}{2}\text{ on both sides}\right)\\ \frac{7}{2}=\frac{7}{3}x\\ \frac{7}{3}x=\frac{7}{2}\left(\text{Switching sides}\right)\\ \frac{3}{7}\cdot \frac{7}{3}x=\frac{7}{2}\cdot \frac{3}{7}\left(\text{Multiplying both sides by }\frac{3}{7}\right)\\ x=\frac{3}{2}=1.5\end{array}$

Therefore, the x -intercept of our given equation is $(1.5,0)$ .

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

  $\begin{array}{l}y=\frac{7}{3}x-\frac{7}{2}\left(\text{Given equation}\right)\\ y=\frac{7}{3}(0)-\frac{7}{2}\left(\text{Substituting }x=0\right)\\ y=0-\frac{7}{2}\\ y=-3.5\end{array}$

Therefore, the y -intercept of our given equation is $(0,-3.5)$ .

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