Precalculus Examples

$x = - 3 + 9 t$ , $y = 7 + 9 t$

Step 1

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

$x = - 3 + 9 t$

Step 2

Rewrite the equation as $- 3 + 9 t = x$ .

$- 3 + 9 t = x$

Step 3

Add $3$ to both sides of the equation.

$9 t = x + 3$

Step 4

Divide each term in $9 t = x + 3$ by $9$ and simplify.

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Step 4.1

Divide each term in $9 t = x + 3$ by $9$ .

$\frac{9 t}{9} = \frac{x}{9} + \frac{3}{9}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $9$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{9 t}{9} = \frac{x}{9} + \frac{3}{9}$

Step 4.2.1.2

Divide $t$ by $1$ .

$t = \frac{x}{9} + \frac{3}{9}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Cancel the common factor of $3$ and $9$ .

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Step 4.3.1.1

Factor $3$ out of $3$ .

$t = \frac{x}{9} + \frac{3 (1)}{9}$

Step 4.3.1.2

Cancel the common factors.

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Step 4.3.1.2.1

Factor $3$ out of $9$ .

$t = \frac{x}{9} + \frac{3 \cdot 1}{3 \cdot 3}$

Step 4.3.1.2.2

Cancel the common factor.

$t = \frac{x}{9} + \frac{3 \cdot 1}{3 \cdot 3}$

Step 4.3.1.2.3

Rewrite the expression.

$t = \frac{x}{9} + \frac{1}{3}$

Step 5

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

$y = 7 + 9 (\frac{x}{9} + \frac{1}{3})$

Step 6

Simplify $7 + 9 (\frac{x}{9} + \frac{1}{3})$ .

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Step 6.1

Simplify each term.

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Step 6.1.1

Apply the distributive property.

$y = 7 + 9 \frac{x}{9} + 9 (\frac{1}{3})$

Step 6.1.2

Cancel the common factor of $9$ .

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Step 6.1.2.1

Cancel the common factor.

$y = 7 + 9 \frac{x}{9} + 9 (\frac{1}{3})$

Step 6.1.2.2

Rewrite the expression.

$y = 7 + x + 9 (\frac{1}{3})$

Step 6.1.3

Cancel the common factor of $3$ .

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Step 6.1.3.1

Factor $3$ out of $9$ .

$y = 7 + x + 3 (3) \frac{1}{3}$

Step 6.1.3.2

Cancel the common factor.

$y = 7 + x + 3 \cdot 3 \frac{1}{3}$

Step 6.1.3.3

Rewrite the expression.

$y = 7 + x + 3$

Step 6.2

Add $7$ and $3$ .

$y = x + 10$