Precalculus Examples

$x (t) = 4 - t$ , $y (t) = 3 t + 2$

Step 1

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

$x = 4 - t$

Step 2

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

$4 - t = x$

Step 3

Subtract $4$ from both sides of the equation.

$- t = x - 4$

Step 4

Divide each term in $- t = x - 4$ by $- 1$ and simplify.

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Step 4.1

Divide each term in $- t = x - 4$ by $- 1$ .

$\frac{- t}{- 1} = \frac{x}{- 1} + \frac{- 4}{- 1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{t}{1} = \frac{x}{- 1} + \frac{- 4}{- 1}$

Step 4.2.2

Divide $t$ by $1$ .

$t = \frac{x}{- 1} + \frac{- 4}{- 1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Move the negative one from the denominator of $\frac{x}{- 1}$ .

$t = - 1 \cdot x + \frac{- 4}{- 1}$

Step 4.3.1.2

Rewrite $- 1 \cdot x$ as $- x$ .

$t = - x + \frac{- 4}{- 1}$

Step 4.3.1.3

Divide $- 4$ by $- 1$ .

$t = - x + 4$

Step 5

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

$y = 3 (- x + 4) + 2$

Step 6

Simplify $3 (- x + 4) + 2$ .

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Step 6.1

Simplify each term.

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Step 6.1.1

Apply the distributive property.

$y = 3 (- x) + 3 \cdot 4 + 2$

Step 6.1.2

Multiply $- 1$ by $3$ .

$y = - 3 x + 3 \cdot 4 + 2$

Step 6.1.3

Multiply $3$ by $4$ .

$y = - 3 x + 12 + 2$

Step 6.2

Add $12$ and $2$ .

$y = - 3 x + 14$