Precalculus Examples

$y = - \frac{1}{4} x + 5$ , $(- 4, 6)$

Step 1

Rewrite in slope-intercept form.

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Step 1.1

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

$y = m x + b$

Step 1.2

Simplify the right side.

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Step 1.2.1

Combine $x$ and $\frac{1}{4}$ .

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

Step 1.3

Write in $y = m x + b$ form.

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Step 1.3.1

Reorder terms.

$y = - (\frac{1}{4} x) + 5$

Step 1.3.2

Remove parentheses.

$y = - \frac{1}{4} x + 5$

Step 2

Using the slope-intercept form, the slope is $- \frac{1}{4}$ .

$m = - \frac{1}{4}$

Step 3

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

Step 4

Use the slope $- \frac{1}{4}$ and a given point $(- 4, 6)$ to substitute for $x_{1}$ and $y_{1}$ in the point-slope form $y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (6) = - \frac{1}{4} \cdot (x - (- 4))$

Step 5

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

$y - 6 = - \frac{1}{4} \cdot (x + 4)$

Step 6

Solve for $y$ .

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Step 6.1

Simplify $- \frac{1}{4} \cdot (x + 4)$ .

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Step 6.1.1

Rewrite.

$y - 6 = 0 + 0 - \frac{1}{4} \cdot (x + 4)$

Step 6.1.2

Simplify by adding zeros.

$y - 6 = - \frac{1}{4} \cdot (x + 4)$

Step 6.1.3

Apply the distributive property.

$y - 6 = - \frac{1}{4} x - \frac{1}{4} \cdot 4$

Step 6.1.4

Combine $x$ and $\frac{1}{4}$ .

$y - 6 = - \frac{x}{4} - \frac{1}{4} \cdot 4$

Step 6.1.5

Cancel the common factor of $4$ .

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Step 6.1.5.1

Move the leading negative in $- \frac{1}{4}$ into the numerator.

$y - 6 = - \frac{x}{4} + \frac{- 1}{4} \cdot 4$

Step 6.1.5.2

Cancel the common factor.

$y - 6 = - \frac{x}{4} + \frac{- 1}{4} \cdot 4$

Step 6.1.5.3

Rewrite the expression.

$y - 6 = - \frac{x}{4} - 1$

Step 6.2

Move all terms not containing $y$ to the right side of the equation.

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Step 6.2.1

Add $6$ to both sides of the equation.

$y = - \frac{x}{4} - 1 + 6$

Step 6.2.2

Add $- 1$ and $6$ .

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

Step 6.3

Write in $y = m x + b$ form.

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Step 6.3.1

Reorder terms.

$y = - (\frac{1}{4} x) + 5$

Step 6.3.2

Remove parentheses.

$y = - \frac{1}{4} x + 5$

Step 7