Pre-Algebra Examples

4 x - 3 y = 12

$4 x - 3 y = 12$

Step 1

Rewrite in slope-intercept form.

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Step 1.1

The slope-intercept form is

y = m x + b

$y = m x + b$ , 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

4 x

$4 x$ from both sides of the equation.

- 3 y = 12 - 4 x

$- 3 y = 12 - 4 x$

Step 1.3

Divide each term in

- 3 y = 12 - 4 x

$- 3 y = 12 - 4 x$ by

- 3

$- 3$ and simplify.

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Step 1.3.1

Divide each term in

- 3 y = 12 - 4 x

$- 3 y = 12 - 4 x$ by

- 3

$- 3$ .

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

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

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of

- 3

$- 3$ .

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Step 1.3.2.1.1

Cancel the common factor.

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

Step 1.3.2.1.2

Divide

$y$ by

$1$ .

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

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

$12$ by

$- 3$ .

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

Step 1.3.3.1.2

Dividing two negative values results in a positive value.

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

Step 1.4

Write in

$y = m x + b$ form.

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Step 1.4.1

Reorder

$- 4$ and

$\frac{4 x}{3}$ .

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

Step 1.4.2

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