Precalculus Examples

$x = 4 t - 5$ , $y = 3 - 8 t$

Step 1

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

$x = 4 t - 5$

Step 2

Rewrite the equation as $4 t - 5 = x$ .

$4 t - 5 = x$

Step 3

Add $5$ to both sides of the equation.

$4 t = x + 5$

Step 4

Divide each term in $4 t = x + 5$ by $4$ and simplify.

Tap for more steps...

Step 4.1

Divide each term in $4 t = x + 5$ by $4$ .

$\frac{4 t}{4} = \frac{x}{4} + \frac{5}{4}$

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.

$\frac{4 t}{4} = \frac{x}{4} + \frac{5}{4}$

Step 4.2.1.2

Divide $t$ by $1$ .

$t = \frac{x}{4} + \frac{5}{4}$

Step 5

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

$y = 3 - 8 (\frac{x}{4} + \frac{5}{4})$

Step 6

Simplify $3 - 8 (\frac{x}{4} + \frac{5}{4})$ .

Tap for more steps...

Step 6.1

Simplify each term.

Tap for more steps...

Step 6.1.1

Apply the distributive property.

$y = 3 - 8 \frac{x}{4} - 8 (\frac{5}{4})$

Step 6.1.2

Cancel the common factor of $4$ .

Tap for more steps...

Step 6.1.2.1

Factor $4$ out of $- 8$ .

$y = 3 + 4 (- 2) \frac{x}{4} - 8 (\frac{5}{4})$

Step 6.1.2.2

Cancel the common factor.

$y = 3 + 4 \cdot - 2 \frac{x}{4} - 8 (\frac{5}{4})$

Step 6.1.2.3

Rewrite the expression.

$y = 3 - 2 x - 8 (\frac{5}{4})$

Step 6.1.3

Cancel the common factor of $4$ .

Tap for more steps...

Step 6.1.3.1

Factor $4$ out of $- 8$ .

$y = 3 - 2 x + 4 (- 2) \frac{5}{4}$

Step 6.1.3.2

Cancel the common factor.

$y = 3 - 2 x + 4 \cdot - 2 \frac{5}{4}$

Step 6.1.3.3

Rewrite the expression.

$y = 3 - 2 x - 2 \cdot 5$

Step 6.1.4

Multiply $- 2$ by $5$ .

$y = 3 - 2 x - 10$

Step 6.2

Subtract $10$ from $3$ .

$y = - 2 x - 7$