Precalculus Examples

$x = 4 t - 3$ , $y = 2 t$

Step 1

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

$x = 4 t - 3$

Step 2

Rewrite the equation as $4 t - 3 = x$ .

$4 t - 3 = x$

Step 3

Add $3$ to both sides of the equation.

$4 t = x + 3$

Step 4

Divide each term in $4 t = x + 3$ by $4$ and simplify.

Tap for more steps...

Step 4.1

Divide each term in $4 t = x + 3$ by $4$ .

$\frac{4 t}{4} = \frac{x}{4} + \frac{3}{4}$

Step 4.2

Simplify the left side.

Tap for more steps...

Step 4.2.1

Cancel the common factor of $4$ .

Tap for more steps...

Step 4.2.1.1

Cancel the common factor.

$\frac{4 t}{4} = \frac{x}{4} + \frac{3}{4}$

Step 4.2.1.2

Divide $t$ by $1$ .

$t = \frac{x}{4} + \frac{3}{4}$

Step 5

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

$y = 2 (\frac{x}{4} + \frac{3}{4})$

Step 6

Simplify $2 (\frac{x}{4} + \frac{3}{4})$ .

Tap for more steps...

Step 6.1

Apply the distributive property.

$y = 2 \frac{x}{4} + 2 (\frac{3}{4})$

Step 6.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 6.2.1

Factor $2$ out of $4$ .

$y = 2 \frac{x}{2 (2)} + 2 (\frac{3}{4})$

Step 6.2.2

Cancel the common factor.

$y = 2 \frac{x}{2 \cdot 2} + 2 (\frac{3}{4})$

Step 6.2.3

Rewrite the expression.

$y = \frac{x}{2} + 2 (\frac{3}{4})$

Step 6.3

Cancel the common factor of $2$ .

Tap for more steps...

Step 6.3.1

Factor $2$ out of $4$ .

$y = \frac{x}{2} + 2 \frac{3}{2 (2)}$

Step 6.3.2

Cancel the common factor.

$y = \frac{x}{2} + 2 \frac{3}{2 \cdot 2}$

Step 6.3.3

Rewrite the expression.

$y = \frac{x}{2} + \frac{3}{2}$