Chapter 2, Problem 1RE

For the following exercises, find the x-intercept and the y-intercept without graphing.

1. $4x-3y=12$

To determine

To Calculate:

The intercepts on the coordinate axes of the straight line with the given equation$4x-3y=12$

Answer to Problem 1RE

  $\begin{array}{l}x-\text{intercept}=3\\ y-\text{intercept}=-4\end{array}$

Explanation of Solution

Given Information:

The equation$4x-3y=12$

Concept used:

If a straight line passes through the points$\left(a,0\right)$(on the$x-axis$) and$\left(0,b\right)$(on the$y-axis$) , we say that the$x-$intercept is$a$and the$y-$intercept is$b$.

The$x-$intercept is found by setting$y=0$and solving for$a$; similarly, the$y-$intercept is found by setting$x=0$and solving for$b$.

Calculation:

For the given equation$4x-3y=12$

  $\begin{array}{l}y=0\Rightarrow 4x=12\Rightarrow x-\text{intercept}=3;\\ x=0\Rightarrow -3y=12\Rightarrow y-\text{intercept}=-4\end{array}$

Conclusion:

For the given line,$x-\text{intercept=3}$and$y-\text{intercept}=-4$