Chapter 13.3, Problem 16PSC

To determine

To find: The point of intersection of V-shaped graph and the graph of a line.

Answer to Problem 16PSC

The point of intersection is $\left(\frac{2}{3},\frac{7}{3}\right)$ .

Explanation of Solution

Given:

The given equations of V-shaped graph is:

  $y=\left|x-3\right|$ .

The given equation of line graph is:

  $y=2x+1\left(a\right)$ .

Calculation:

The graph of the above equations is given below:

  

From the graph it is clear that:

The line intersect at the left side of the V-shaped graph, which has the equation $y=-x+3\left(b\right)$

The point of intersection is calculated as:

  $\begin{array}{c}-x+3=2x+1\left[\text{put equation}\left(a\right)=\text{equation}\left(b\right)\right]\\ 3x=2\\ x=\frac{2}{3}\\ y=2\left(\frac{2}{3}\right)+1\left[\text{substitute }x=\frac{2}{3}\text{in equation }\left(a\right)\right]\end{array}$

Further simplified as:

  $y=\frac{7}{3}$

Therefore the point of intersection is $\left(\frac{2}{3},\frac{7}{3}\right)$ .