Pre-Algebra Examples

$6 x - 5 y + 3 = 2 x - 2 y - 9$

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

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

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Step 1.2.1

Add $2 y$ to both sides of the equation.

$6 x - 5 y + 3 + 2 y = 2 x - 9$

Step 1.2.2

Add $- 5 y$ and $2 y$ .

$6 x - 3 y + 3 = 2 x - 9$

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 $6 x$ from both sides of the equation.

$- 3 y + 3 = 2 x - 9 - 6 x$

Step 1.3.2

Subtract $3$ from both sides of the equation.

$- 3 y = 2 x - 9 - 6 x - 3$

Step 1.3.3

Subtract $6 x$ from $2 x$ .

$- 3 y = - 4 x - 9 - 3$

Step 1.3.4

Subtract $3$ from $- 9$ .

$- 3 y = - 4 x - 12$

Step 1.4

Divide each term in $- 3 y = - 4 x - 12$ by $- 3$ and simplify.

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Step 1.4.1

Divide each term in $- 3 y = - 4 x - 12$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{- 4 x}{- 3} + \frac{- 12}{- 3}$

Step 1.4.2

Simplify the left side.

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Step 1.4.2.1

Cancel the common factor of $- 3$ .

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Step 1.4.2.1.1

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{- 4 x}{- 3} + \frac{- 12}{- 3}$

Step 1.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 4 x}{- 3} + \frac{- 12}{- 3}$

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

Dividing two negative values results in a positive value.

$y = \frac{4 x}{3} + \frac{- 12}{- 3}$

Step 1.4.3.1.2

Divide $- 12$ by $- 3$ .

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

Step 1.5

Reorder terms.

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

Step 2

Using the slope-intercept form, the slope is $\frac{4}{3}$ .

$m = \frac{4}{3}$

Step 3