Chapter 1.2, Problem 27E

To determine

The $x-\text{intercept}$ and $y-\text{intercept}$ of the graph of the equation $y=\left|3x-7\right|$ .

Answer to Problem 27E

The $x-\text{intercept}$ of the graph is the point $\left(x,y\right)=\left(\frac{7}{3},0\right)$

The $y-\text{intercept}$ of the graph is the point $\left(x,y\right)=\left(0,7\right)$

Explanation of Solution

Given:

The equation $y=\left|3x-7\right|$

Concept Used:

The $x-\text{intercept}$ is a point on the graph where the graph intersects $x-\text{axis}$ i.e., where the $y$ coordinate is zero.

The $y-\text{intercept}$ is a point on the graph where the graph intersects $y-\text{axis}$ i.e., where the $x$ coordinate is zero.

Calculation:

Given the equation $y=\left|3x-7\right|$

For $x-\text{intercept}$ , substituting $y=0$

i.e., $y=\left|3x-7\right|$

i.e., $\begin{array}{c}0=\left|3x-7\right|\\ 0=3x-7\\ x=\frac{7}{3}\end{array}$

Therefore, $x-\text{intercept}$ of the graph is the point $\left(x,y\right)=\left(\frac{7}{3},0\right)$

For $y-\text{intercept}$ , substituting $x=0$

i.e., $y=\left|3x-7\right|$

i.e., $\begin{array}{l}y=\left|3\left(0\right)-7\right|\\ y=\left|-7\right|\\ y=7\end{array}$

which is not defined for real number.

Therefore, $y-\text{intercept}$ of the graph is the point $\left(x,y\right)=\left(0,7\right)$