Finite Math Examples

$y = (\frac{8}{9}) (x - 4) - 8$

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 $(\frac{8}{9}) (x - 4) - 8$ .

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Step 1.2.1.1

Simplify each term.

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Step 1.2.1.1.1

Apply the distributive property.

$y = \frac{8}{9} x + \frac{8}{9} \cdot - 4 - 8$

Step 1.2.1.1.2

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

$y = \frac{8 x}{9} + \frac{8}{9} \cdot - 4 - 8$

Step 1.2.1.1.3

Multiply $\frac{8}{9} \cdot - 4$ .

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Step 1.2.1.1.3.1

Combine $\frac{8}{9}$ and $- 4$ .

$y = \frac{8 x}{9} + \frac{8 \cdot - 4}{9} - 8$

Step 1.2.1.1.3.2

Multiply $8$ by $- 4$ .

$y = \frac{8 x}{9} + \frac{- 32}{9} - 8$

Step 1.2.1.1.4

Move the negative in front of the fraction.

$y = \frac{8 x}{9} - \frac{32}{9} - 8$

Step 1.2.1.2

To write $- 8$ as a fraction with a common denominator, multiply by $\frac{9}{9}$ .

$y = \frac{8 x}{9} - \frac{32}{9} - 8 \cdot \frac{9}{9}$

Step 1.2.1.3

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

$y = \frac{8 x}{9} - \frac{32}{9} + \frac{- 8 \cdot 9}{9}$

Step 1.2.1.4

Combine the numerators over the common denominator.

$y = \frac{8 x}{9} + \frac{- 32 - 8 \cdot 9}{9}$

Step 1.2.1.5

Simplify the numerator.

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Step 1.2.1.5.1

Multiply $- 8$ by $9$ .

$y = \frac{8 x}{9} + \frac{- 32 - 72}{9}$

Step 1.2.1.5.2

Subtract $72$ from $- 32$ .

$y = \frac{8 x}{9} + \frac{- 104}{9}$

Step 1.2.1.6

Move the negative in front of the fraction.

$y = \frac{8 x}{9} - \frac{104}{9}$

Step 1.3

Reorder terms.

$y = \frac{8}{9} x - \frac{104}{9}$

Step 2

Use the slope-intercept form to find the slope and y-intercept.

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Step 2.1

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = \frac{8}{9}$

$b = - \frac{104}{9}$

Step 2.2

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $\frac{8}{9}$

y-intercept: $(0, - \frac{104}{9})$

Slope: $\frac{8}{9}$

y-intercept: $(0, - \frac{104}{9})$

Step 3