Pre-Algebra Examples

$y - 1 = (\frac{- 4}{9}) (x - 5)$

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 $(\frac{- 4}{9}) (x - 5)$ .

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Step 1.2.1.1

Move the negative in front of the fraction.

$y - 1 = - \frac{4}{9} (x - 5)$

Step 1.2.1.2

Apply the distributive property.

$y - 1 = - \frac{4}{9} x - \frac{4}{9} \cdot - 5$

Step 1.2.1.3

Combine $x$ and $\frac{4}{9}$ .

$y - 1 = - \frac{x \cdot 4}{9} - \frac{4}{9} \cdot - 5$

Step 1.2.1.4

Multiply $- \frac{4}{9} \cdot - 5$ .

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Step 1.2.1.4.1

Multiply $- 5$ by $- 1$ .

$y - 1 = - \frac{x \cdot 4}{9} + 5 (\frac{4}{9})$

Step 1.2.1.4.2

Combine $5$ and $\frac{4}{9}$ .

$y - 1 = - \frac{x \cdot 4}{9} + \frac{5 \cdot 4}{9}$

Step 1.2.1.4.3

Multiply $5$ by $4$ .

$y - 1 = - \frac{x \cdot 4}{9} + \frac{20}{9}$

Step 1.2.1.5

Move $4$ to the left of $x$ .

$y - 1 = - \frac{4 x}{9} + \frac{20}{9}$

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 $1$ to both sides of the equation.

$y = - \frac{4 x}{9} + \frac{20}{9} + 1$

Step 1.3.2

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

$y = - \frac{4 x}{9} + \frac{20}{9} + \frac{9}{9}$

Step 1.3.3

Combine the numerators over the common denominator.

$y = - \frac{4 x}{9} + \frac{20 + 9}{9}$

Step 1.3.4

Add $20$ and $9$ .

$y = - \frac{4 x}{9} + \frac{29}{9}$

Step 1.4

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

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Step 1.4.1

Reorder terms.

$y = - (\frac{4}{9} x) + \frac{29}{9}$

Step 1.4.2

Remove parentheses.

$y = - \frac{4}{9} x + \frac{29}{9}$

Step 2

Using the slope-intercept form, the y-intercept is $\frac{29}{9}$ .

$b = \frac{29}{9}$

Step 3

y-intercept in point form.

$(0, \frac{29}{9})$

Step 4