Chapter 13.6, Problem 5CE

To determine

To find : the $x$ and $y$ -intercept of the line

Answer to Problem 5CE

The $x$ -intercept is $-6$ and $y$ -intercept is $8$

Explanation of Solution

Given information : The equation of line is $-4x+3y=24$

Calculation :

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

  $\begin{array}{l}-4x+3y=24\\ \Rightarrow -4\left(0\right)+3\left(b\right)=24\\ \Rightarrow 0+3b=24\\ \Rightarrow 3b=24\\ \Rightarrow b=\frac{24}{3}\\ \Rightarrow b=8\end{array}$

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

  $\begin{array}{l}-4x+3y=24\\ \Rightarrow -4\left(a\right)+3\left(0\right)=24\\ \Rightarrow -4a+0=24\\ \Rightarrow -4a=24\\ \Rightarrow a=\frac{24}{-4}\\ \Rightarrow a=-6\end{array}$