Find the x and y Intercepts |x-2|

$| x - 2 |$

Step 1

Write $| x - 2 |$ as an equation.

$y = | x - 2 |$

Step 2

Find the x-intercepts.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = | x - 2 |$

Solve the equation.

Rewrite the equation as $| x - 2 | = 0$ .

$| x - 2 | = 0$

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$x - 2 = \pm 0$

Plus or minus $0$ is $0$ .

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$x - 2 = \pm 0$

Plus or minus $0$ is $0$ .

$x - 2 = 0$

Add $2$ to both sides of the equation.

$x = 2$

x-intercept(s) in point form.

x-intercept(s): $(2, 0)$

Step 3

Find the y-intercepts.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = | (0) - 2 |$

Simplify $| (0) - 2 |$ .

Subtract $2$ from $0$ .

$y = | - 2 |$

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

$y = 2$

y-intercept(s) in point form.

y-intercept(s): $(0, 2)$

Step 4

List the intersections.

x-intercept(s): $(2, 0)$

y-intercept(s): $(0, 2)$

Step 5