Chapter 13.1, Problem 9PSA

To determine

To find: Whether the point $\left(-4,6\right)$ lie on the graph of $y=\left|x-2\right|$ .

Answer to Problem 9PSA

The point $\left(-4,6\right)$ does not lie on the graph of $y=\left|x-2\right|$ .

Explanation of Solution

Given:

The equation is $y=\left|x-2\right|$ and point is $\left(-4,6\right)$ .

Calculation:

The point $\left(-4,6\right)$ will lie on the graph of equation $y=\left|x-2\right|$ if it satisfies the equation.

Substitute $-4$ for $x$ , and $6$ for $y$ in the equation $y=\left|x-2\right|$ .

  $\begin{array}{c}6=\left|-4-2\right|\\ 6=\left|-6\right|\\ 6=6\end{array}$

The point $\left(-4,6\right)$ satisfies the equation.

Therefore, the point $\left(-4,6\right)$ does not lie on the graph of $y=\left|x-2\right|$ .