Chapter 7.4, Problem 1QR

Solution

To calculate: The $x$ and $y$ intercept of a line $2x-3y=6$ and also draw its graph.

The obtained intercept points are $\left(3,0\right)$, $\left(0,-2\right)$ .

  

Given Information:

The equation of a line is $2x-3y=6$ .

Calculation:

Consider the equation of line.

The $x$ -intercept of a line is in the form of $\left(a,0\right)$ . To obtain the $x$ -intercept of a line, put $y=0$ in the given equation of a line and solve for $x$ .

  $\begin{array}{c}2x-3\left(0\right)=6\\ 2x=6\end{array}$

Now, divide both the sides of the obtained equation by 2.

  $\begin{array}{c}\frac{2x}{2}=\frac{6}{2}\\ x=3\end{array}$

The $x$ -intercept of a line is $\left(3,0\right)$ .

The $y$ -intercept of a line is in the form of $\left(0,b\right)$ . To obtain the $y$ -intercept of a line, put $x=0$ in the given equation of a line and solve for $y$ .

  $\begin{array}{c}2\left(0\right)-3y=6\\ -3y=6\end{array}$

Now, divide both the sides of the obtained equation by $-3$ .

  $\begin{array}{c}\frac{-3y}{-3}=\frac{6}{-3}\\ y=-2\end{array}$

The $y$ -intercept of a line is $\left(0,-2\right)$ .

Draw the graph of a line $2x-3y=6$ .

  

Therefore, the obtained intercept points are $\left(3,0\right)$, $\left(0,-2\right)$ .