Calculus Examples

$x = 2 t + 2$ , $y = t$

Step 1

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

$x = 2 t + 2$

Step 2

Rewrite the equation as $2 t + 2 = x$ .

$2 t + 2 = x$

Step 3

Subtract $2$ from both sides of the equation.

$2 t = x - 2$

Step 4

Divide each term in $2 t = x - 2$ by $2$ and simplify.

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Step 4.1

Divide each term in $2 t = x - 2$ by $2$ .

$\frac{2 t}{2} = \frac{x}{2} + \frac{- 2}{2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{2 t}{2} = \frac{x}{2} + \frac{- 2}{2}$

Step 4.2.1.2

Divide $t$ by $1$ .

$t = \frac{x}{2} + \frac{- 2}{2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 2$ by $2$ .

$t = \frac{x}{2} - 1$

Step 5

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

$y = \frac{x}{2} - 1$

Step 6

Remove parentheses.

$y = \frac{x}{2} - 1$

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