Precalculus Examples

$y - 9 = \frac{1}{5} (x - 2)$

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

Simplify $\frac{1}{5} (x - 2)$ .

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Step 1.2.1.1

Apply the distributive property.

$y - 9 = \frac{1}{5} x + \frac{1}{5} \cdot - 2$

Step 1.2.1.2

Combine $\frac{1}{5}$ and $x$ .

$y - 9 = \frac{x}{5} + \frac{1}{5} \cdot - 2$

Step 1.2.1.3

Combine $\frac{1}{5}$ and $- 2$ .

$y - 9 = \frac{x}{5} + \frac{- 2}{5}$

Step 1.2.1.4

Move the negative in front of the fraction.

$y - 9 = \frac{x}{5} - \frac{2}{5}$

Step 1.3

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

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Step 1.3.1

Add $9$ to both sides of the equation.

$y = \frac{x}{5} - \frac{2}{5} + 9$

Step 1.3.2

To write $9$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$y = \frac{x}{5} - \frac{2}{5} + 9 \cdot \frac{5}{5}$

Step 1.3.3

Combine $9$ and $\frac{5}{5}$ .

$y = \frac{x}{5} - \frac{2}{5} + \frac{9 \cdot 5}{5}$

Step 1.3.4

Combine the numerators over the common denominator.

$y = \frac{x}{5} + \frac{- 2 + 9 \cdot 5}{5}$

Step 1.3.5

Simplify the numerator.

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Step 1.3.5.1

Multiply $9$ by $5$ .

$y = \frac{x}{5} + \frac{- 2 + 45}{5}$

Step 1.3.5.2

Add $- 2$ and $45$ .

$y = \frac{x}{5} + \frac{43}{5}$

Step 1.4

Reorder terms.

$y = \frac{1}{5} x + \frac{43}{5}$

Step 2

Using the slope-intercept form, the slope is $\frac{1}{5}$ .

$m = \frac{1}{5}$

Step 3