Pre-Algebra Examples

$1 - 3 (y - 2 x) = 37 + 3 (x - 4 y)$

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 each term.

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Step 1.2.1.1

Apply the distributive property.

$1 - 3 y - 3 (- 2 x) = 37 + 3 (x - 4 y)$

Step 1.2.1.2

Multiply $- 2$ by $- 3$ .

$1 - 3 y + 6 x = 37 + 3 (x - 4 y)$

Step 1.3

Simplify the right side.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Apply the distributive property.

$1 - 3 y + 6 x = 37 + 3 x + 3 (- 4 y)$

Step 1.3.1.2

Multiply $- 4$ by $3$ .

$1 - 3 y + 6 x = 37 + 3 x - 12 y$

Step 1.4

Move all terms containing $y$ to the left side of the equation.

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Step 1.4.1

Add $12 y$ to both sides of the equation.

$1 - 3 y + 6 x + 12 y = 37 + 3 x$

Step 1.4.2

Add $- 3 y$ and $12 y$ .

$1 + 6 x + 9 y = 37 + 3 x$

Step 1.5

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

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Step 1.5.1

Subtract $1$ from both sides of the equation.

$6 x + 9 y = 37 + 3 x - 1$

Step 1.5.2

Subtract $6 x$ from both sides of the equation.

$9 y = 37 + 3 x - 1 - 6 x$

Step 1.5.3

Subtract $1$ from $37$ .

$9 y = 3 x + 36 - 6 x$

Step 1.5.4

Subtract $6 x$ from $3 x$ .

$9 y = - 3 x + 36$

Step 1.6

Divide each term in $9 y = - 3 x + 36$ by $9$ and simplify.

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Step 1.6.1

Divide each term in $9 y = - 3 x + 36$ by $9$ .

$\frac{9 y}{9} = \frac{- 3 x}{9} + \frac{36}{9}$

Step 1.6.2

Simplify the left side.

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Step 1.6.2.1

Cancel the common factor of $9$ .

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Step 1.6.2.1.1

Cancel the common factor.

$\frac{9 y}{9} = \frac{- 3 x}{9} + \frac{36}{9}$

Step 1.6.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 3 x}{9} + \frac{36}{9}$

Step 1.6.3

Simplify the right side.

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Step 1.6.3.1

Simplify each term.

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Step 1.6.3.1.1

Cancel the common factor of $- 3$ and $9$ .

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Step 1.6.3.1.1.1

Factor $3$ out of $- 3 x$ .

$y = \frac{3 (- x)}{9} + \frac{36}{9}$

Step 1.6.3.1.1.2

Cancel the common factors.

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Step 1.6.3.1.1.2.1

Factor $3$ out of $9$ .

$y = \frac{3 (- x)}{3 (3)} + \frac{36}{9}$

Step 1.6.3.1.1.2.2

Cancel the common factor.

$y = \frac{3 (- x)}{3 \cdot 3} + \frac{36}{9}$

Step 1.6.3.1.1.2.3

Rewrite the expression.

$y = \frac{- x}{3} + \frac{36}{9}$

Step 1.6.3.1.2

Move the negative in front of the fraction.

$y = - \frac{x}{3} + \frac{36}{9}$

Step 1.6.3.1.3

Divide $36$ by $9$ .

$y = - \frac{x}{3} + 4$

Step 1.7

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

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Step 1.7.1

Reorder terms.

$y = - (\frac{1}{3} x) + 4$

Step 1.7.2

Remove parentheses.

$y = - \frac{1}{3} x + 4$

Step 2

Using the slope-intercept form, the slope is $- \frac{1}{3}$ .

$m = - \frac{1}{3}$

Step 3