Precalculus Examples

$x = t - 4$ , $y = \frac{t}{2} - 5$

Step 1

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

$x = t - 4$

Step 2

Rewrite the equation as $t - 4 = x$ .

$t - 4 = x$

Step 3

Add $4$ to both sides of the equation.

$t = x + 4$

Step 4

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

$y = \frac{x + 4}{2} - 5$

Step 5

Simplify $\frac{x + 4}{2} - 5$ .

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Step 5.1

To write $- 5$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = \frac{x + 4}{2} - 5 \cdot \frac{2}{2}$

Step 5.2

Simplify terms.

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Step 5.2.1

Combine $- 5$ and $\frac{2}{2}$ .

$y = \frac{x + 4}{2} + \frac{- 5 \cdot 2}{2}$

Step 5.2.2

Combine the numerators over the common denominator.

$y = \frac{x + 4 - 5 \cdot 2}{2}$

Step 5.3

Simplify the numerator.

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Step 5.3.1

Multiply $- 5$ by $2$ .

$y = \frac{x + 4 - 10}{2}$

Step 5.3.2

Subtract $10$ from $4$ .

$y = \frac{x - 6}{2}$