Pre-Algebra Examples

$y - 7 = \frac{1}{9} \cdot (x - 5)$

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 $\frac{1}{9} \cdot (x - 5)$ .

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Step 1.2.1.1

Apply the distributive property.

$y - 7 = \frac{1}{9} x + \frac{1}{9} \cdot - 5$

Step 1.2.1.2

Combine $\frac{1}{9}$ and $x$ .

$y - 7 = \frac{x}{9} + \frac{1}{9} \cdot - 5$

Step 1.2.1.3

Combine $\frac{1}{9}$ and $- 5$ .

$y - 7 = \frac{x}{9} + \frac{- 5}{9}$

Step 1.2.1.4

Move the negative in front of the fraction.

$y - 7 = \frac{x}{9} - \frac{5}{9}$

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 $7$ to both sides of the equation.

$y = \frac{x}{9} - \frac{5}{9} + 7$

Step 1.3.2

To write $7$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$y = \frac{x}{9} - \frac{5}{9} + 7 \cdot \frac{9}{9}$

Step 1.3.3

Combine $7$ and $\frac{9}{9}$ .

$y = \frac{x}{9} - \frac{5}{9} + \frac{7 \cdot 9}{9}$

Step 1.3.4

Combine the numerators over the common denominator.

$y = \frac{x}{9} + \frac{- 5 + 7 \cdot 9}{9}$

Step 1.3.5

Simplify the numerator.

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Step 1.3.5.1

Multiply $7$ by $9$ .

$y = \frac{x}{9} + \frac{- 5 + 63}{9}$

Step 1.3.5.2

Add $- 5$ and $63$ .

$y = \frac{x}{9} + \frac{58}{9}$

Step 1.4

Reorder terms.

$y = \frac{1}{9} x + \frac{58}{9}$

Step 2

Using the slope-intercept form, the y-intercept is $\frac{58}{9}$ .

$b = \frac{58}{9}$

Step 3

y-intercept in point form.

$(0, \frac{58}{9})$

Step 4