Chapter 7.4, Problem 2QR

Solution

To calculate: The $x$ and $y$ intercept of a line $5x+10y=30$ and also draw its graph.

The obtained intercept are $\left(6,0\right)$and $\left(0,3\right)$ .

  

Given Information:

The equation of a line is $5x+10y=30$ .

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 $x$ .

  $\begin{array}{c}5x+10\left(0\right)=30\\ 5x=30\end{array}$

Now, divide both the sides of the obtained equation by 5.

  $\begin{array}{c}\frac{5x}{5}=\frac{30}{5}\\ x=6\end{array}$

The $x$ -intercept of a line is $\left(6,0\right)$ .

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 $y$ .

  $\begin{array}{c}5\left(0\right)+10y=30\\ 10y=30\end{array}$

Now, divide both the sides of the obtained equation by 10.

  $\begin{array}{c}\frac{10y}{10}=\frac{30}{10}\\ y=3\end{array}$

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

Draw the graph of a line $5x+10y=30$ .