Precalculus Examples

$x = | t - 1 |$ , $y = t + 2$

Step 1

Set up the parametric equation for $x (t)$ to solve the equation for $t$ .

$x = | t - 1 |$

Step 2

Rewrite the equation as $| t - 1 | = x$ .

$| t - 1 | = x$

Step 3

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

$t - 1 = \pm x$

Step 4

The complete solution is the result of both the positive and negative portions of the solution.

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Step 4.1

First, use the positive value of the $\pm$ to find the first solution.

$t - 1 = x$

Step 4.2

Add $1$ to both sides of the equation.

$t = x + 1$

Step 4.3

Next, use the negative value of the $\pm$ to find the second solution.

$t - 1 = - x$

Step 4.4

Add $1$ to both sides of the equation.

$t = - x + 1$

Step 4.5

The complete solution is the result of both the positive and negative portions of the solution.

$t = x + 1$

$t = - x + 1$

$t = x + 1$

$t = - x + 1$

Step 5

Replace $t$ in the equation for $y$ to get the equation in terms of $x$ .

$y = (x + 1, - x + 1) + 2$