Algebra Examples

$6 x + - 2 y = 18$

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 $1 \cdot - 1 = - 1$

$6 x - 2 y = 18$

Step 2

Rewrite in slope-intercept form.

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Step 2.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 2.2

Simplify the left side.

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Step 2.2.1

Add $6 x$ and $- 2 y$ .

$6 x - 2 y = 18$

Step 2.3

Subtract $6 x$ from both sides of the equation.

$- 2 y = 18 - 6 x$

Step 2.4

Divide each term in $- 2 y = 18 - 6 x$ by $- 2$ and simplify.

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Step 2.4.1

Divide each term in $- 2 y = 18 - 6 x$ by $- 2$ .

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

Step 2.4.2

Simplify the left side.

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Step 2.4.2.1

Cancel the common factor of $- 2$ .

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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