Precalculus Examples

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

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

Step 1

Choose a point that the parallel line will pass through.

(0, 0)

$(0, 0)$

Step 2

Rewrite in slope-intercept form.

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Step 2.1

The slope-intercept form is

y = m x + b

$y = m x + b$ , where

m

$m$ is the slope and

b

$b$ is the y-intercept.

y = m x + b

$y = m x + b$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

Combine

x

$x$ and

\frac{3}{2}

$\frac{3}{2}$ .

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

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

Step 2.2.1.2

Move

3

$3$ to the left of

x

$x$ .

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

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

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

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

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

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

Step 2.3

Write in

y = m x + b

$y = m x + b$ form.

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Step 2.3.1

Reorder terms.

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

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

Step 2.3.2

Remove parentheses.

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

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

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

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

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

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

Step 3

Using the slope-intercept form, the slope is

- \frac{3}{2}

$- \frac{3}{2}$ .

m = - \frac{3}{2}

$m = - \frac{3}{2}$

Step 4

To find an equation that is parallel, the slopes must be equal. Find the parallel line using the point-slope formula.

Step 5

Use the slope

- \frac{3}{2}

$- \frac{3}{2}$ and a given point

(0, 0)

$(0, 0)$ to substitute for

x_{1}

$x_{1}$ and

y_{1}

$y_{1}$ in the point-slope form

y - y_{1} = m (x - x_{1})

$y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation

m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

y - (0) = - \frac{3}{2} \cdot (x - (0))

$y - (0) = - \frac{3}{2} \cdot (x - (0))$

Step 6

Simplify the equation and keep it in point-slope form.

y + 0 = - \frac{3}{2} \cdot (x + 0)

$y + 0 = - \frac{3}{2} \cdot (x + 0)$

Step 7

Solve for

y

$y$ .

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Step 7.1

Add

y

$y$ and

0

$0$ .

y = - \frac{3}{2} \cdot (x + 0)

$y = - \frac{3}{2} \cdot (x + 0)$

Step 7.2

Simplify

- \frac{3}{2} \cdot (x + 0)

$- \frac{3}{2} \cdot (x + 0)$ .

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Step 7.2.1

Add

x

$x$ and

0

$0$ .

y = - \frac{3}{2} \cdot x

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

Step 7.2.2

Combine

x

$x$ and

\frac{3}{2}

$\frac{3}{2}$ .

y = - \frac{x \cdot 3}{2}

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

Step 7.2.3

Move

3

$3$ to the left of

x

$x$ .

y = - \frac{3 x}{2}

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

y = - \frac{3 x}{2}

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

Step 7.3

Write in

y = m x + b

$y = m x + b$ form.

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Step 7.3.1

Reorder terms.

y = - (\frac{3}{2} x)

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

Step 7.3.2

Remove parentheses.

y = - \frac{3}{2} x

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

y = - \frac{3}{2} x

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

y = - \frac{3}{2} x

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

Step 8

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