Calculus Examples

$x (t) = t - \frac{1}{2}$ , $y (t) = t + 6$

Step 1

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

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

Step 2

Rewrite the equation as $t - \frac{1}{2} = x$ .

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

Step 3

Add $\frac{1}{2}$ to both sides of the equation.

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

Step 4

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

$y = (x + \frac{1}{2}) + 6$

Step 5

Remove parentheses.

$y = x + \frac{1}{2} + 6$

Step 6

Remove parentheses.

$y = (x + \frac{1}{2}) + 6$

Step 7

Simplify $(x + \frac{1}{2}) + 6$ .

Tap for more steps...

Step 7.1

To write $6$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = x + \frac{1}{2} + 6 \cdot \frac{2}{2}$

Step 7.2

Combine $6$ and $\frac{2}{2}$ .

$y = x + \frac{1}{2} + \frac{6 \cdot 2}{2}$

Step 7.3

Combine the numerators over the common denominator.

$y = x + \frac{1 + 6 \cdot 2}{2}$

Step 7.4

Simplify the numerator.

Tap for more steps...

Step 7.4.1

Multiply $6$ by $2$ .

$y = x + \frac{1 + 12}{2}$

Step 7.4.2

Add $1$ and $12$ .

$y = x + \frac{13}{2}$