Graph Using a Table of Values y=|x-4|

$y = | x - 4 |$

Substitute $- 2$ for $x$ and find the result for $y$ .

$y = | (- 2) - 4 |$

Simplify $| (- 2) - 4 |$ .

Subtract $4$ from $- 2$ .

$y = | - 6 |$

The absolute value is the distance between a number and zero. The distance between $- 6$ and $0$ is $6$ .

$y = 6$

Substitute $- 1$ for $x$ and find the result for $y$ .

$y = | (- 1) - 4 |$

Simplify $| (- 1) - 4 |$ .

Subtract $4$ from $- 1$ .

$y = | - 5 |$

The absolute value is the distance between a number and zero. The distance between $- 5$ and $0$ is $5$ .

$y = 5$

Substitute $0$ for $x$ and find the result for $y$ .

$y = | (0) - 4 |$

Simplify $| (0) - 4 |$ .

Subtract $4$ from $0$ .

$y = | - 4 |$

The absolute value is the distance between a number and zero. The distance between $- 4$ and $0$ is $4$ .

$y = 4$

Substitute $1$ for $x$ and find the result for $y$ .

$y = | (1) - 4 |$

Simplify $| (1) - 4 |$ .

Subtract $4$ from $1$ .

$y = | - 3 |$

The absolute value is the distance between a number and zero. The distance between $- 3$ and $0$ is $3$ .

$y = 3$

Substitute $2$ for $x$ and find the result for $y$ .

$y = | (2) - 4 |$

Simplify $| (2) - 4 |$ .

Subtract $4$ from $2$ .

$y = | - 2 |$

The absolute value is the distance between a number and zero. The distance between $- 2$ and $0$ is $2$ .

$y = 2$

This is a table of possible values to use when graphing the equation.

$\begin{array}{c} x & y \\ - 2 & 6 \\ - 1 & 5 \\ 0 & 4 \\ 1 & 3 \\ 2 & 2 \end{array}$