Graph Using a Table of Values y=|x-3|

$y = | x - 3 |$

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

$y = | (- 2) - 3 |$

Simplify $| (- 2) - 3 |$ .

Subtract $3$ from $- 2$ .

$y = | - 5 |$

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

$y = 5$

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

$y = | (- 1) - 3 |$

Simplify $| (- 1) - 3 |$ .

Subtract $3$ from $- 1$ .

$y = | - 4 |$

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

$y = 4$

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

$y = | (0) - 3 |$

Simplify $| (0) - 3 |$ .

Subtract $3$ from $0$ .

$y = | - 3 |$

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

$y = 3$

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

$y = | (1) - 3 |$

Simplify $| (1) - 3 |$ .

Subtract $3$ from $1$ .

$y = | - 2 |$

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

$y = 2$

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

$y = | (2) - 3 |$

Simplify $| (2) - 3 |$ .

Subtract $3$ from $2$ .

$y = | - 1 |$

The absolute value is the distance between a number and zero. The distance between $- 1$ and $0$ is $1$ .

$y = 1$

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

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