Precalculus Examples

$y - 1 = - \frac{1}{6} \cdot (x - 7)$

Step 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 2

Rewrite in slope-intercept form.

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Step 2.1

Simplify the right side.

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Step 2.1.1

Simplify $- \frac{1}{6} \cdot (x - 7)$ .

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Step 2.1.1.1

Apply the distributive property.

$y - 1 = - \frac{1}{6} x - \frac{1}{6} \cdot - 7$

Step 2.1.1.2

Combine $x$ and $\frac{1}{6}$ .

$y - 1 = - \frac{x}{6} - \frac{1}{6} \cdot - 7$

Step 2.1.1.3

Multiply $- \frac{1}{6} \cdot - 7$ .

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Step 2.1.1.3.1

Multiply $- 7$ by $- 1$ .

$y - 1 = - \frac{x}{6} + 7 (\frac{1}{6})$

Step 2.1.1.3.2

Combine $7$ and $\frac{1}{6}$ .

$y - 1 = - \frac{x}{6} + \frac{7}{6}$

Step 2.2

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

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Step 2.2.1

Add $1$ to both sides of the equation.

$y = - \frac{x}{6} + \frac{7}{6} + 1$

Step 2.2.2

Write $1$ as a fraction with a common denominator.

$y = - \frac{x}{6} + \frac{7}{6} + \frac{6}{6}$

Step 2.2.3

Combine the numerators over the common denominator.

$y = - \frac{x}{6} + \frac{7 + 6}{6}$

Step 2.2.4

Add $7$ and $6$ .

$y = - \frac{x}{6} + \frac{13}{6}$

Step 2.3

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

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Step 2.3.1

Reorder terms.

$y = - (\frac{1}{6} x) + \frac{13}{6}$

Step 2.3.2

Remove parentheses.

$y = - \frac{1}{6} x + \frac{13}{6}$