Pre-Algebra Examples

$y - (- 1) = \frac{8}{9} \cdot (x - (- 1))$

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 left side.

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Step 1.2.1

Multiply $- 1$ by $- 1$ .

$y + 1 = \frac{8}{9} \cdot (x - (- 1))$

Step 1.3

Simplify the right side.

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Step 1.3.1

Simplify $\frac{8}{9} \cdot (x - (- 1))$ .

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Step 1.3.1.1

Multiply $- 1$ by $- 1$ .

$y + 1 = \frac{8}{9} \cdot (x + 1)$

Step 1.3.1.2

Apply the distributive property.

$y + 1 = \frac{8}{9} x + \frac{8}{9} \cdot 1$

Step 1.3.1.3

Combine $\frac{8}{9}$ and $x$ .

$y + 1 = \frac{8 x}{9} + \frac{8}{9} \cdot 1$

Step 1.3.1.4

Multiply $\frac{8}{9}$ by $1$ .

$y + 1 = \frac{8 x}{9} + \frac{8}{9}$

Step 1.4

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

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Step 1.4.1

Subtract $1$ from both sides of the equation.

$y = \frac{8 x}{9} + \frac{8}{9} - 1$

Step 1.4.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$y = \frac{8 x}{9} + \frac{8}{9} - 1 \cdot \frac{9}{9}$

Step 1.4.3

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

$y = \frac{8 x}{9} + \frac{8}{9} + \frac{- 1 \cdot 9}{9}$

Step 1.4.4

Combine the numerators over the common denominator.

$y = \frac{8 x}{9} + \frac{8 - 1 \cdot 9}{9}$

Step 1.4.5

Simplify the numerator.

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Step 1.4.5.1

Multiply $- 1$ by $9$ .

$y = \frac{8 x}{9} + \frac{8 - 9}{9}$

Step 1.4.5.2

Subtract $9$ from $8$ .

$y = \frac{8 x}{9} + \frac{- 1}{9}$

Step 1.4.6

Move the negative in front of the fraction.

$y = \frac{8 x}{9} - \frac{1}{9}$

Step 1.5

Reorder terms.

$y = \frac{8}{9} x - \frac{1}{9}$

Step 2

Using the slope-intercept form, the y-intercept is $- \frac{1}{9}$ .

$b = - \frac{1}{9}$

Step 3

y-intercept in point form.

$(0, - \frac{1}{9})$

Step 4