Chapter 7.4, Problem 4QR

Solution

To calculate: The $x$ and $y$ intercept of a line $\frac{x}{30}-\frac{y}{20}=1$ and also draw its graph.

The obtained intercepts are $\left(30,0\right)$; $\left(0,-20\right)$ and the required graph is drown below,

  

Given Information:

The equation of a line is $\frac{x}{30}-\frac{y}{20}=1$ .

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 $x$ .

  $\begin{array}{c}\frac{x}{30}-\frac{0}{20}=1\\ \frac{x}{30}=1\end{array}$

Now, multiply both the sides of the obtained equation by 30.

  $\begin{array}{c}30\left(\frac{x}{30}\right)=30\left(1\right)\\ x=30\end{array}$

The $x$ -intercept of a line is $\left(30,0\right)$ .

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 $y$ .

  $\begin{array}{c}\frac{0}{30}-\frac{y}{20}=1\\ -\frac{y}{20}=1\end{array}$

Now, multiply both the sides of the obtained equation by $-20$ .

  $\begin{array}{c}-20\left(-\frac{y}{20}\right)=-20\left(1\right)\\ y=-20\end{array}$

The $y$ -intercept of a line is $\left(0,-20\right)$ .

Draw the graph of a line $\frac{x}{30}-\frac{y}{20}=1$ .