Chapter 8, Problem 10CR

To determine

To find:

The intercepts of theequation’s graph.

Answer to Problem 10CR

The x-intercept of our given equation would be $5$ .

The y-intercept of our given equation would be $-10$ .

Explanation of Solution

Given:

An equation:

  $y=2x-10$

Calculation:

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

  $\begin{array}{l}y=2x-10\left(\text{Given equation}\right)\\ 0=2x-10\left(\text{Substituting }y=0\right)\\ 2x-10=0\left(\text{Switching sides}\right)\\ 2x-10+10=0+10\left(\text{Adding 10 on both sides}\right)\\ 2x=10\\ \frac{2x}{2}=\frac{10}{2}\left(\text{Dividing both sides by 2}\right)\\ x=5\end{array}$

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

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

  $\begin{array}{l}y=2x-10\left(\text{Given equation}\right)\\ y=2(0)-10\left(\text{Substituting }x=0\right)\\ y=0-10\\ y=-10\end{array}$

Therefore, the y-intercept of our given equation is $-10$ .