Pre-Algebra Examples

$8 y = - 6 x - 4$

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

Divide each term in $8 y = - 6 x - 4$ by $8$ and simplify.

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Step 1.2.1

Divide each term in $8 y = - 6 x - 4$ by $8$ .

$\frac{8 y}{8} = \frac{- 6 x}{8} + \frac{- 4}{8}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $8$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{8 y}{8} = \frac{- 6 x}{8} + \frac{- 4}{8}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 6 x}{8} + \frac{- 4}{8}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Cancel the common factor of $- 6$ and $8$ .

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Step 1.2.3.1.1.1

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

$y = \frac{2 (- 3 x)}{8} + \frac{- 4}{8}$

Step 1.2.3.1.1.2

Cancel the common factors.

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Step 1.2.3.1.1.2.1

Factor $2$ out of $8$ .

$y = \frac{2 (- 3 x)}{2 (4)} + \frac{- 4}{8}$

Step 1.2.3.1.1.2.2

Cancel the common factor.

$y = \frac{2 (- 3 x)}{2 \cdot 4} + \frac{- 4}{8}$

Step 1.2.3.1.1.2.3

Rewrite the expression.

$y = \frac{- 3 x}{4} + \frac{- 4}{8}$

Step 1.2.3.1.2

Move the negative in front of the fraction.

$y = - \frac{3 x}{4} + \frac{- 4}{8}$

Step 1.2.3.1.3

Cancel the common factor of $- 4$ and $8$ .

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Step 1.2.3.1.3.1

Factor $4$ out of $- 4$ .

$y = - \frac{3 x}{4} + \frac{4 (- 1)}{8}$

Step 1.2.3.1.3.2

Cancel the common factors.

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Step 1.2.3.1.3.2.1

Factor $4$ out of $8$ .

$y = - \frac{3 x}{4} + \frac{4 \cdot - 1}{4 \cdot 2}$

Step 1.2.3.1.3.2.2

Cancel the common factor.

$y = - \frac{3 x}{4} + \frac{4 \cdot - 1}{4 \cdot 2}$

Step 1.2.3.1.3.2.3

Rewrite the expression.

$y = - \frac{3 x}{4} + \frac{- 1}{2}$

Step 1.2.3.1.4

Move the negative in front of the fraction.

$y = - \frac{3 x}{4} - \frac{1}{2}$

Step 1.3

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

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Step 1.3.1

Reorder terms.

$y = - (\frac{3}{4} x) - \frac{1}{2}$

Step 1.3.2

Remove parentheses.

$y = - \frac{3}{4} x - \frac{1}{2}$

Step 2

Using the slope-intercept form, the slope is $- \frac{3}{4}$ .

$m = - \frac{3}{4}$

Step 3