Algebra Examples

$3 x - 4 y = 8$

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

Subtract $3 x$ from both sides of the equation.

$- 4 y = 8 - 3 x$

Step 1.3

Divide each term in $- 4 y = 8 - 3 x$ by $- 4$ and simplify.

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Step 1.3.1

Divide each term in $- 4 y = 8 - 3 x$ by $- 4$ .

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

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $- 4$ .

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Step 1.3.2.1.1

Cancel the common factor.

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

Step 1.3.2.1.2

Divide $y$ by $1$ .

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

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

Divide $8$ by $- 4$ .

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

Step 1.3.3.1.2

Dividing two negative values results in a positive value.

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

Step 1.4

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

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Step 1.4.1

Reorder $- 2$ and $\frac{3 x}{4}$ .

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

Step 1.4.2

Reorder terms.

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

Step 2

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

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

Step 3