Chapter 13.6, Problem 9WE

To determine

To find : the $x$ and $y$ -intercept of the line and also graph the equation.

Answer to Problem 9WE

The $x$ -intercept is $4$ and $y$ -intercept is $6$ .

Explanation of Solution

Given information : The equation of line is $3x+2y=12$ .

Calculation :

When $x=0\&y=b$ . So, $b$ is the $y$ -intercept.

  $\begin{array}{l}3x+2y=12\\ \Rightarrow 3\left(0\right)+2\left(b\right)=12\\ \Rightarrow 0+2b=12\\ \Rightarrow 2b=12\\ \Rightarrow b=\frac{12}{2}\\ \Rightarrow b=6\end{array}$

When $x=a\&y=0$ . So, $b$ is the $x$ -intercept.

  $\begin{array}{l}3x+2y=12\\ \Rightarrow 3\left(a\right)+2\left(0\right)=12\\ \Rightarrow 3a+0=12\\ \Rightarrow 3a=12\\ \Rightarrow a=\frac{12}{3}\\ \Rightarrow a=4\end{array}$

The graph will be shown below: