Algebra Examples

$12 x - 8 y + 7 = 9$

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

Move all terms not containing $y$ to the right side of the equation.

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Step 1.2.1

Subtract $12 x$ from both sides of the equation.

$- 8 y + 7 = 9 - 12 x$

Step 1.2.2

Subtract $7$ from both sides of the equation.

$- 8 y = 9 - 12 x - 7$

Step 1.2.3

Subtract $7$ from $9$ .

$- 8 y = - 12 x + 2$

Step 1.3

Divide each term in $- 8 y = - 12 x + 2$ by $- 8$ and simplify.

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Step 1.3.1

Divide each term in $- 8 y = - 12 x + 2$ by $- 8$ .

$\frac{- 8 y}{- 8} = \frac{- 12 x}{- 8} + \frac{2}{- 8}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $- 8$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{- 8 y}{- 8} = \frac{- 12 x}{- 8} + \frac{2}{- 8}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 12 x}{- 8} + \frac{2}{- 8}$

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 $- 12$ and $- 8$ .

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Step 1.3.3.1.1.1

Factor $- 4$ out of $- 12 x$ .

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

Step 1.3.3.1.1.2

Cancel the common factors.

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Step 1.3.3.1.1.2.1

Factor $- 4$ out of $- 8$ .

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

Step 1.3.3.1.1.2.2

Cancel the common factor.

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

Step 1.3.3.1.1.2.3

Rewrite the expression.

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

Step 1.3.3.1.2

Cancel the common factor of $2$ and $- 8$ .

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Step 1.3.3.1.2.1

Factor $2$ out of $2$ .

$y = \frac{3 x}{2} + \frac{2 (1)}{- 8}$

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 $- 8$ .

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

Step 1.3.3.1.2.2.2

Cancel the common factor.

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

Step 1.3.3.1.2.2.3

Rewrite the expression.

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

Step 1.3.3.1.3

Move the negative in front of the fraction.

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

Step 1.4

Reorder terms.

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

Step 2

Using the slope-intercept form, the slope is $\frac{3}{2}$ .

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

Step 3