Chapter 8, Problem 7MCQ

To determine

To find:

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

Answer to Problem 7MCQ

The x-intercept of our given equation would be $2$ .

The y-intercept of our given equation would be $4$ .

Explanation of Solution

Given:

An equation:

  $6x+3y=12$

Calculation:

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

  $\begin{array}{l}6x+3y=12\left(\text{Given equation}\right)\\ 6x+3(0)=12\left(\text{Substituting }y=0\right)\\ 6x=12\\ \frac{6x}{6}=\frac{12}{6}\left(\text{Dividing both sides by 6}\right)\\ x=2\end{array}$

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

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

  $\begin{array}{l}6x+3y=12\left(\text{Given equation}\right)\\ 6(0)+3y=12\left(\text{Substituting }x=0\right)\\ 3y=12\\ \frac{3y}{3}=\frac{12}{3}\left(\text{Dividing both sides by 3}\right)\\ y=4\end{array}$

Therefore, the y-intercept of our given equation is $4$ .

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