Pre-Algebra Examples

$- 2 x - 6 y = - 16$

Step 1

Rewrite in slope-intercept form.

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Step 1.1

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 1.2

Add $2 x$ to both sides of the equation.

$- 6 y = - 16 + 2 x$

Step 1.3

Divide each term in $- 6 y = - 16 + 2 x$ by $- 6$ and simplify.

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Step 1.3.1

Divide each term in $- 6 y = - 16 + 2 x$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{- 16}{- 6} + \frac{2 x}{- 6}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $- 6$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{- 16}{- 6} + \frac{2 x}{- 6}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 16}{- 6} + \frac{2 x}{- 6}$

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

Cancel the common factor of $- 16$ and $- 6$ .

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Step 1.3.3.1.1.1

Factor $- 2$ out of $- 16$ .

$y = \frac{- 2 (8)}{- 6} + \frac{2 x}{- 6}$

Step 1.3.3.1.1.2

Cancel the common factors.

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Step 1.3.3.1.1.2.1

Factor $- 2$ out of $- 6$ .

$y = \frac{- 2 \cdot 8}{- 2 \cdot 3} + \frac{2 x}{- 6}$

Step 1.3.3.1.1.2.2

Cancel the common factor.

$y = \frac{- 2 \cdot 8}{- 2 \cdot 3} + \frac{2 x}{- 6}$

Step 1.3.3.1.1.2.3

Rewrite the expression.

$y = \frac{8}{3} + \frac{2 x}{- 6}$

Step 1.3.3.1.2

Cancel the common factor of $2$ and $- 6$ .

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Step 1.3.3.1.2.1

Factor $2$ out of $2 x$ .

$y = \frac{8}{3} + \frac{2 (x)}{- 6}$

Step 1.3.3.1.2.2

Cancel the common factors.

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Step 1.3.3.1.2.2.1

Factor $2$ out of $- 6$ .

$y = \frac{8}{3} + \frac{2 x}{2 \cdot - 3}$

Step 1.3.3.1.2.2.2

Cancel the common factor.

$y = \frac{8}{3} + \frac{2 x}{2 \cdot - 3}$

Step 1.3.3.1.2.2.3

Rewrite the expression.

$y = \frac{8}{3} + \frac{x}{- 3}$

Step 1.3.3.1.3

Move the negative in front of the fraction.

$y = \frac{8}{3} - \frac{x}{3}$

Step 1.4

Write in $y = m x + b$ form.

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Step 1.4.1

Reorder $\frac{8}{3}$ and $- \frac{x}{3}$ .

$y = - \frac{x}{3} + \frac{8}{3}$

Step 1.4.2

Reorder terms.

$y = - (\frac{1}{3} x) + \frac{8}{3}$

Step 1.4.3

Remove parentheses.

$y = - \frac{1}{3} x + \frac{8}{3}$

Step 2

Using the slope-intercept form, the slope is $- \frac{1}{3}$ .

$m = - \frac{1}{3}$

Step 3