Algebra Examples

6 x + - 2 y = 18

$6 x + - 2 y = 18$

Step 1

Replace all occurrences of

+

$+$

-

$-$ with a single

-

$-$ . A plus sign followed by a minus sign has the same mathematical meaning as a single minus sign because

1 \cdot - 1 = - 1

$1 \cdot - 1 = - 1$

6 x - 2 y = 18

$6 x - 2 y = 18$

Step 2

Rewrite in slope-intercept form.

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Step 2.1

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 2.2

Simplify the left side.

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Step 2.2.1

Add

6 x

$6 x$ and

- 2 y

$- 2 y$ .

6 x - 2 y = 18

$6 x - 2 y = 18$

6 x - 2 y = 18

$6 x - 2 y = 18$

Step 2.3

Subtract

6 x

$6 x$ from both sides of the equation.

- 2 y = 18 - 6 x

$- 2 y = 18 - 6 x$

Step 2.4

Divide each term in

- 2 y = 18 - 6 x

$- 2 y = 18 - 6 x$ by

- 2

$- 2$ and simplify.

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Step 2.4.1

Divide each term in

- 2 y = 18 - 6 x

$- 2 y = 18 - 6 x$ by

- 2

$- 2$ .

\frac{- 2 y}{- 2} = \frac{18}{- 2} + \frac{- 6 x}{- 2}

$\frac{- 2 y}{- 2} = \frac{18}{- 2} + \frac{- 6 x}{- 2}$

Step 2.4.2

Simplify the left side.

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Step 2.4.2.1

Cancel the common factor of

- 2

$- 2$ .

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Step 2.4.2.1.1

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{18}{- 2} + \frac{- 6 x}{- 2}$

Step 2.4.2.1.2

Divide

$y$ by

$1$ .

$y = \frac{18}{- 2} + \frac{- 6 x}{- 2}$

Step 2.4.3

Simplify the right side.

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Step 2.4.3.1

Simplify each term.

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Step 2.4.3.1.1

Divide

$18$ by

$- 2$ .

$y = - 9 + \frac{- 6 x}{- 2}$

Step 2.4.3.1.2

Cancel the common factor of

$- 6$ and

$- 2$ .

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Step 2.4.3.1.2.1

Factor

$- 2$ out of

$- 6 x$ .

$y = - 9 + \frac{- 2 (3 x)}{- 2}$

Step 2.4.3.1.2.2

Cancel the common factors.

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Step 2.4.3.1.2.2.1

Factor

$- 2$ out of

$- 2$ .

$y = - 9 + \frac{- 2 (3 x)}{- 2 (1)}$

Step 2.4.3.1.2.2.2

Cancel the common factor.

$y = - 9 + \frac{- 2 (3 x)}{- 2 \cdot 1}$

Step 2.4.3.1.2.2.3

Rewrite the expression.

$y = - 9 + \frac{3 x}{1}$

Step 2.4.3.1.2.2.4

Divide

$3 x$ by

$1$ .

$y = - 9 + 3 x$

Step 2.5

Reorder

$- 9$ and

$3 x$ .

$y = 3 x - 9$

Step 3

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

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Step 3.1

Find the values of

$m$ and

$b$ using the form

$y = m x + b$ .

$m = 3$

$b = - 9$

Step 3.2

The slope of the line is the value of

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

$b$ .

Slope:

$3$

y-intercept:

$(0, - 9)$

Slope:

$3$

y-intercept:

$(0, - 9)$

Step 4