Chapter 13.6, Problem 12WE

To determine

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

Answer to Problem 12WE

The $x$ -intercept is $-6$ and $y$ -intercept is $-\frac{9}{2}$ .

Explanation of Solution

Given information : The equation of line is $3x+4y=-18$ .

Calculation :

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

  $\begin{array}{l}3x+4y=-18\\ \Rightarrow 3\left(0\right)+4\left(b\right)=-18\\ \Rightarrow 0+4b=-18\\ \Rightarrow 4b=-18\\ \Rightarrow b=\frac{-18}{4}\\ \Rightarrow b=-\frac{9}{2}\end{array}$

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

  $\begin{array}{l}3x+4y=-18\\ \Rightarrow 3\left(a\right)+4\left(0\right)=-18\\ \Rightarrow 3a+0=-18\\ \Rightarrow 3a=-18\\ \Rightarrow a=\frac{-18}{3}\\ \Rightarrow a=-6\end{array}$

The graph will be shown below: