Pre-Algebra Examples

$\frac{y - 3}{6} - \frac{y - 4}{5} = - \frac{1}{6}$

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

Simplify $\frac{y - 3}{6} - \frac{y - 4}{5}$ .

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Step 1.2.1.1

To write $\frac{y - 3}{6}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{y - 3}{6} \cdot \frac{5}{5} - \frac{y - 4}{5} = - \frac{1}{6}$

Step 1.2.1.2

To write $- \frac{y - 4}{5}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$\frac{y - 3}{6} \cdot \frac{5}{5} - \frac{y - 4}{5} \cdot \frac{6}{6} = - \frac{1}{6}$

Step 1.2.1.3

Write each expression with a common denominator of $30$ , by multiplying each by an appropriate factor of $1$ .

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Step 1.2.1.3.1

Multiply $\frac{y - 3}{6}$ by $\frac{5}{5}$ .

$\frac{(y - 3) \cdot 5}{6 \cdot 5} - \frac{y - 4}{5} \cdot \frac{6}{6} = - \frac{1}{6}$

Step 1.2.1.3.2

Multiply $6$ by $5$ .

$\frac{(y - 3) \cdot 5}{30} - \frac{y - 4}{5} \cdot \frac{6}{6} = - \frac{1}{6}$

Step 1.2.1.3.3

Multiply $\frac{y - 4}{5}$ by $\frac{6}{6}$ .

$\frac{(y - 3) \cdot 5}{30} - \frac{(y - 4) \cdot 6}{5 \cdot 6} = - \frac{1}{6}$

Step 1.2.1.3.4

Multiply $5$ by $6$ .

$\frac{(y - 3) \cdot 5}{30} - \frac{(y - 4) \cdot 6}{30} = - \frac{1}{6}$

Step 1.2.1.4

Combine the numerators over the common denominator.

$\frac{(y - 3) \cdot 5 - (y - 4) \cdot 6}{30} = - \frac{1}{6}$

Step 1.2.1.5

Simplify the numerator.

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Step 1.2.1.5.1

Apply the distributive property.

$\frac{y \cdot 5 - 3 \cdot 5 - (y - 4) \cdot 6}{30} = - \frac{1}{6}$

Step 1.2.1.5.2

Move $5$ to the left of $y$ .

$\frac{5 \cdot y - 3 \cdot 5 - (y - 4) \cdot 6}{30} = - \frac{1}{6}$

Step 1.2.1.5.3

Multiply $- 3$ by $5$ .

$\frac{5 \cdot y - 15 - (y - 4) \cdot 6}{30} = - \frac{1}{6}$

Step 1.2.1.5.4

Apply the distributive property.

$\frac{5 y - 15 + (- y - - 4) \cdot 6}{30} = - \frac{1}{6}$

Step 1.2.1.5.5

Multiply $- 1$ by $- 4$ .

$\frac{5 y - 15 + (- y + 4) \cdot 6}{30} = - \frac{1}{6}$

Step 1.2.1.5.6

Apply the distributive property.

$\frac{5 y - 15 - y \cdot 6 + 4 \cdot 6}{30} = - \frac{1}{6}$

Step 1.2.1.5.7

Multiply $6$ by $- 1$ .

$\frac{5 y - 15 - 6 y + 4 \cdot 6}{30} = - \frac{1}{6}$

Step 1.2.1.5.8

Multiply $4$ by $6$ .

$\frac{5 y - 15 - 6 y + 24}{30} = - \frac{1}{6}$

Step 1.2.1.5.9

Subtract $6 y$ from $5 y$ .

$\frac{- y - 15 + 24}{30} = - \frac{1}{6}$

Step 1.2.1.5.10

Add $- 15$ and $24$ .

$\frac{- y + 9}{30} = - \frac{1}{6}$

Step 1.2.1.6

Simplify with factoring out.

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Step 1.2.1.6.1

Factor $- 1$ out of $- y$ .

$\frac{- (y) + 9}{30} = - \frac{1}{6}$

Step 1.2.1.6.2

Rewrite $9$ as $- 1 (- 9)$ .

$\frac{- (y) - 1 (- 9)}{30} = - \frac{1}{6}$

Step 1.2.1.6.3

Factor $- 1$ out of $- (y) - 1 (- 9)$ .

$\frac{- (y - 9)}{30} = - \frac{1}{6}$

Step 1.2.1.6.4

Simplify the expression.

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Step 1.2.1.6.4.1

Rewrite $- (y - 9)$ as $- 1 (y - 9)$ .

$\frac{- 1 (y - 9)}{30} = - \frac{1}{6}$

Step 1.2.1.6.4.2

Move the negative in front of the fraction.

$- \frac{y - 9}{30} = - \frac{1}{6}$

Step 1.3

Multiply both sides of the equation by $- 30$ .

$- 30 (- \frac{y - 9}{30}) = - 30 (- \frac{1}{6})$

Step 1.4

Simplify both sides of the equation.

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Step 1.4.1

Simplify the left side.

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Step 1.4.1.1

Simplify $- 30 (- \frac{y - 9}{30})$ .

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Step 1.4.1.1.1

Cancel the common factor of $30$ .

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Step 1.4.1.1.1.1

Move the leading negative in $- \frac{y - 9}{30}$ into the numerator.

$- 30 \frac{- (y - 9)}{30} = - 30 (- \frac{1}{6})$

Step 1.4.1.1.1.2

Factor $30$ out of $- 30$ .

$30 (- 1) \frac{- (y - 9)}{30} = - 30 (- \frac{1}{6})$

Step 1.4.1.1.1.3

Cancel the common factor.

$30 \cdot - 1 \frac{- (y - 9)}{30} = - 30 (- \frac{1}{6})$

Step 1.4.1.1.1.4

Rewrite the expression.

$- - (y - 9) = - 30 (- \frac{1}{6})$

Step 1.4.1.1.2

Multiply.

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Step 1.4.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 (y - 9) = - 30 (- \frac{1}{6})$

Step 1.4.1.1.2.2

Multiply $y - 9$ by $1$ .

$y - 9 = - 30 (- \frac{1}{6})$

Step 1.4.2

Simplify the right side.

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Step 1.4.2.1

Simplify $- 30 (- \frac{1}{6})$ .

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Step 1.4.2.1.1

Cancel the common factor of $6$ .

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Step 1.4.2.1.1.1

Move the leading negative in $- \frac{1}{6}$ into the numerator.

$y - 9 = - 30 (\frac{- 1}{6})$

Step 1.4.2.1.1.2

Factor $6$ out of $- 30$ .

$y - 9 = 6 (- 5) \frac{- 1}{6}$

Step 1.4.2.1.1.3

Cancel the common factor.

$y - 9 = 6 \cdot - 5 \frac{- 1}{6}$

Step 1.4.2.1.1.4

Rewrite the expression.

$y - 9 = - 5 \cdot - 1$

Step 1.4.2.1.2

Multiply $- 5$ by $- 1$ .

$y - 9 = 5$

Step 1.5

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

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Step 1.5.1

Add $9$ to both sides of the equation.

$y = 5 + 9$

Step 1.5.2

Add $5$ and $9$ .

$y = 14$

Step 2

Using the slope-intercept form, the y-intercept is $14$ .

$b = 14$

Step 3

y-intercept in point form.

$(0, 14)$

Step 4