Algebra Examples

2 x - 3 y = 12

$2 x - 3 y = 12$

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

2 x

$2 x$ from both sides of the equation.

- 3 y = 12 - 2 x

$- 3 y = 12 - 2 x$

Step 1.3

Divide each term in

- 3 y = 12 - 2 x

$- 3 y = 12 - 2 x$ by

- 3

$- 3$ and simplify.

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Step 1.3.1

Divide each term in

- 3 y = 12 - 2 x

$- 3 y = 12 - 2 x$ by

- 3

$- 3$ .

\frac{- 3 y}{- 3} = \frac{12}{- 3} + \frac{- 2 x}{- 3}

$\frac{- 3 y}{- 3} = \frac{12}{- 3} + \frac{- 2 x}{- 3}$

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{- 2 x}{- 3}

$\frac{- 3 y}{- 3} = \frac{12}{- 3} + \frac{- 2 x}{- 3}$

Step 1.3.2.1.2

Divide

y

$y$ by

1

$1$ .

y = \frac{12}{- 3} + \frac{- 2 x}{- 3}

$y = \frac{12}{- 3} + \frac{- 2 x}{- 3}$

y = \frac{12}{- 3} + \frac{- 2 x}{- 3}

$y = \frac{12}{- 3} + \frac{- 2 x}{- 3}$

y = \frac{12}{- 3} + \frac{- 2 x}{- 3}

$y = \frac{12}{- 3} + \frac{- 2 x}{- 3}$

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

$12$ by

- 3

$- 3$ .

y = - 4 + \frac{- 2 x}{- 3}

$y = - 4 + \frac{- 2 x}{- 3}$

Step 1.3.3.1.2

Dividing two negative values results in a positive value.

y = - 4 + \frac{2 x}{3}

$y = - 4 + \frac{2 x}{3}$

y = - 4 + \frac{2 x}{3}

$y = - 4 + \frac{2 x}{3}$

y = - 4 + \frac{2 x}{3}

$y = - 4 + \frac{2 x}{3}$

y = - 4 + \frac{2 x}{3}

$y = - 4 + \frac{2 x}{3}$

Step 1.4

Write in

y = m x + b

$y = m x + b$ form.

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Step 1.4.1

Reorder

- 4

$- 4$ and

\frac{2 x}{3}

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

y = \frac{2 x}{3} - 4

$y = \frac{2 x}{3} - 4$

Step 1.4.2

Reorder terms.

y = \frac{2}{3} x - 4

$y = \frac{2}{3} x - 4$

y = \frac{2}{3} x - 4

$y = \frac{2}{3} x - 4$

y = \frac{2}{3} x - 4

$y = \frac{2}{3} x - 4$

Step 2

Use the slope-intercept form to find the slope and y-intercept.

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Step 2.1

Find the values of

m

$m$ and

b

$b$ using the form

y = m x + b

$y = m x + b$ .

m = \frac{2}{3}

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

b = - 4

$b = - 4$

Step 2.2

The slope of the line is the value of

m

$m$ , and the y-intercept is the value of

b

$b$ .

Slope:

\frac{2}{3}

$\frac{2}{3}$

y-intercept:

(0, - 4)

$(0, - 4)$

Slope:

\frac{2}{3}

$\frac{2}{3}$

y-intercept:

(0, - 4)

$(0, - 4)$

Step 3