Chapter 1, Problem 41RE

To determine

To find: the intercept and graph the line.

Answer to Problem 41RE

The $x$ -intercept is 6 and a point on the graph of the equation is (6, 0)

The $y$ -intercept is -4 and a point on the graph of the equation is $(0,-4)$

  

Explanation of Solution

Given:

  $2x-3y=12$

Calculation:

For obtaining the x-intercept, let $y=0$ in the equation and solve for $x$ .

  $\begin{array}{l}2x-3y=12\\ 2x-3(0)=12\\ 2x=12\end{array}$

Divide both sides of the equation by 2

  $\begin{array}{l}\frac{2x}{2}=\frac{12}{2}\\ x=6\end{array}$

So, the $x$ -intercept is 6 and a point on the graph of the equation is (6, 0)

For obtaining the $y$ -intercept, let $x=0$ in the equation and solve for $x$ .

  $\begin{array}{l}2x-3y=12\\ 2(0)-3y=1\\ 2-3y=12\end{array}$

Divide by -3 on both sides of the equation.

  $\begin{array}{l}\frac{-3y}{-3}=\frac{12}{-3}\\ y=-4\end{array}$

So, the $y$ -intercept is -4 and a point on the graph of the equation is $(0,-4)$ .

The line can be graphed by plotting the points and drawing a line passing through them.

  

Conclusion:

Therefore, the $x$ -intercept is 6 and the $y$ -intercept is -4