Finite Math Examples

$p = 13 x + 10 y + 12$

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

Rewrite the equation as $13 x + 10 y + 12 = p$ .

$13 x + 10 y + 12 = p$

Step 1.3

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

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Step 1.3.1

Subtract $13 x$ from both sides of the equation.

$10 y + 12 = p - 13 x$

Step 1.3.2

Subtract $12$ from both sides of the equation.

$10 y = p - 13 x - 12$

Step 1.4

Divide each term in $10 y = p - 13 x - 12$ by $10$ and simplify.

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Step 1.4.1

Divide each term in $10 y = p - 13 x - 12$ by $10$ .

$\frac{10 y}{10} = \frac{p}{10} + \frac{- 13 x}{10} + \frac{- 12}{10}$

Step 1.4.2

Simplify the left side.

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Step 1.4.2.1

Cancel the common factor of $10$ .

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Step 1.4.2.1.1

Cancel the common factor.

$\frac{10 y}{10} = \frac{p}{10} + \frac{- 13 x}{10} + \frac{- 12}{10}$

Step 1.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{p}{10} + \frac{- 13 x}{10} + \frac{- 12}{10}$

Step 1.4.3

Simplify the right side.

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Step 1.4.3.1

Simplify each term.

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Step 1.4.3.1.1

Move the negative in front of the fraction.

$y = \frac{p}{10} - \frac{13 x}{10} + \frac{- 12}{10}$

Step 1.4.3.1.2

Cancel the common factor of $- 12$ and $10$ .

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Step 1.4.3.1.2.1

Factor $2$ out of $- 12$ .

$y = \frac{p}{10} - \frac{13 x}{10} + \frac{2 (- 6)}{10}$

Step 1.4.3.1.2.2

Cancel the common factors.

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Step 1.4.3.1.2.2.1

Factor $2$ out of $10$ .

$y = \frac{p}{10} - \frac{13 x}{10} + \frac{2 \cdot - 6}{2 \cdot 5}$

Step 1.4.3.1.2.2.2

Cancel the common factor.

$y = \frac{p}{10} - \frac{13 x}{10} + \frac{2 \cdot - 6}{2 \cdot 5}$

Step 1.4.3.1.2.2.3

Rewrite the expression.

$y = \frac{p}{10} - \frac{13 x}{10} + \frac{- 6}{5}$

Step 1.4.3.1.3

Move the negative in front of the fraction.

$y = \frac{p}{10} - \frac{13 x}{10} - \frac{6}{5}$

Step 1.5

Combine $- \frac{13 x}{10} - \frac{6}{5}$ .

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Step 1.5.1

To write $- \frac{6}{5}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = \frac{p}{10} - \frac{13 x}{10} - \frac{6}{5} \cdot \frac{2}{2}$

Step 1.5.2

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.5.2.1

Multiply $\frac{6}{5}$ by $\frac{2}{2}$ .

$y = \frac{p}{10} - \frac{13 x}{10} - \frac{6 \cdot 2}{5 \cdot 2}$

Step 1.5.2.2

Multiply $5$ by $2$ .

$y = \frac{p}{10} - \frac{13 x}{10} - \frac{6 \cdot 2}{10}$

Step 1.5.3

Combine the numerators over the common denominator.

$y = \frac{p}{10} + \frac{- 13 x - 6 \cdot 2}{10}$

Step 1.5.4

Multiply $- 6$ by $2$ .

$y = \frac{p}{10} + \frac{- 13 x - 12}{10}$

Step 1.5.5

Factor $- 1$ out of $- 13 x$ .

$y = \frac{p}{10} + \frac{- (13 x) - 12}{10}$

Step 1.5.6

Rewrite $- 12$ as $- 1 (12)$ .

$y = \frac{p}{10} + \frac{- (13 x) - 1 \cdot 12}{10}$

Step 1.5.7

Factor $- 1$ out of $- (13 x) - 1 (12)$ .

$y = \frac{p}{10} + \frac{- (13 x + 12)}{10}$

Step 1.5.8

Simplify the expression.

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Step 1.5.8.1

Rewrite $- (13 x + 12)$ as $- 1 (13 x + 12)$ .

$y = \frac{p}{10} + \frac{- 1 (13 x + 12)}{10}$

Step 1.5.8.2

Move the negative in front of the fraction.

$y = \frac{p}{10} - \frac{13 x + 12}{10}$

Step 1.6

Rewrite in slope-intercept form.

$y = \frac{1}{10} p - \frac{13 x + 12}{10}$

Step 2

The slope and y-intercept cannot be found for this problem since it is not linear.

Not Linear

Step 3

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

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Step 3.1

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

$m =$

$b =$

Step 3.2

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

Slope:

y-intercept: $(0,)$

Slope:

y-intercept: $(0,)$

Step 4