Algebra Examples

3 x - 2 y = 2

$3 x - 2 y = 2$

Step 1

Rewrite in slope-intercept form.

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Step 1.1

The slope-intercept form is

y = m x + b

$y = m x + b$ , where

m

$m$ is the slope and

b

$b$ is the y-intercept.

y = m x + b

$y = m x + b$

Step 1.2

Subtract

3 x

$3 x$ from both sides of the equation.

- 2 y = 2 - 3 x

$- 2 y = 2 - 3 x$

Step 1.3

Divide each term in

- 2 y = 2 - 3 x

$- 2 y = 2 - 3 x$ by

- 2

$- 2$ and simplify.

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Step 1.3.1

Divide each term in

- 2 y = 2 - 3 x

$- 2 y = 2 - 3 x$ by

- 2

$- 2$ .

\frac{- 2 y}{- 2} = \frac{2}{- 2} + \frac{- 3 x}{- 2}

$\frac{- 2 y}{- 2} = \frac{2}{- 2} + \frac{- 3 x}{- 2}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of

- 2

$- 2$ .

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Step 1.3.2.1.1

Cancel the common factor.

\frac{- 2 y}{- 2} = \frac{2}{- 2} + \frac{- 3 x}{- 2}

$\frac{- 2 y}{- 2} = \frac{2}{- 2} + \frac{- 3 x}{- 2}$

Step 1.3.2.1.2

Divide

y

$y$ by

1

$1$ .

y = \frac{2}{- 2} + \frac{- 3 x}{- 2}

$y = \frac{2}{- 2} + \frac{- 3 x}{- 2}$

y = \frac{2}{- 2} + \frac{- 3 x}{- 2}

$y = \frac{2}{- 2} + \frac{- 3 x}{- 2}$

y = \frac{2}{- 2} + \frac{- 3 x}{- 2}

$y = \frac{2}{- 2} + \frac{- 3 x}{- 2}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Simplify each term.

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Step 1.3.3.1.1

Divide

2

$2$ by

- 2

$- 2$ .

y = - 1 + \frac{- 3 x}{- 2}

$y = - 1 + \frac{- 3 x}{- 2}$

Step 1.3.3.1.2

Dividing two negative values results in a positive value.

y = - 1 + \frac{3 x}{2}

$y = - 1 + \frac{3 x}{2}$

y = - 1 + \frac{3 x}{2}

$y = - 1 + \frac{3 x}{2}$

y = - 1 + \frac{3 x}{2}

$y = - 1 + \frac{3 x}{2}$

y = - 1 + \frac{3 x}{2}

$y = - 1 + \frac{3 x}{2}$

Step 1.4

Write in

y = m x + b

$y = m x + b$ form.

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Step 1.4.1

Reorder

- 1

$- 1$ and

\frac{3 x}{2}

$\frac{3 x}{2}$ .

y = \frac{3 x}{2} - 1

$y = \frac{3 x}{2} - 1$

Step 1.4.2

Reorder terms.

y = \frac{3}{2} x - 1

$y = \frac{3}{2} x - 1$

y = \frac{3}{2} x - 1

$y = \frac{3}{2} x - 1$

y = \frac{3}{2} x - 1

$y = \frac{3}{2} x - 1$

Step 2

Using the slope-intercept form, the slope is

\frac{3}{2}

$\frac{3}{2}$ .

m = \frac{3}{2}

$m = \frac{3}{2}$

Step 3