Precalculus Examples

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

Choose a point that the parallel line will pass through.

$(0, 0)$

Rewrite in slope-intercept form.

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The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Simplify each term.

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Combine $x$ and $\frac{3}{2}$ .

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

Move $3$ to the left of $x$ .

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

Rewrite in slope-intercept form.

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

Using the slope-intercept form, the slope is $- \frac{3}{2}$ .

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

To find an equation that is parallel to $y = - \frac{3}{2} x + 3$ , the slopes must be equal. Using the slope of the equation, find the parallel line using the point-slope formula.

$(0, 0)$

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

Using the point-slope form $y - y_{1} = m (x - x_{1})$ , plug in $m = - \frac{3}{2}$ , $x_{1} = 0$ , and $y_{1} = 0$ .

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

Solve for $y$ .

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Subtract $0$ from $y$ .

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

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

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Subtract $0$ from $x$ .

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

Combine $x$ and $\frac{3}{2}$ .

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

Move $3$ to the left of $x$ .

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

Reorder terms.

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

Remove parentheses.

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

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