Pre-Algebra Examples

$5 x + 6 y - 30 = 0$

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 $5 x$ from both sides of the equation.

$6 y - 30 = - 5 x$

Step 1.2.2

Add $30$ to both sides of the equation.

$6 y = - 5 x + 30$

Step 1.3

Divide each term in $6 y = - 5 x + 30$ by $6$ and simplify.

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Step 1.3.1

Divide each term in $6 y = - 5 x + 30$ by $6$ .

$\frac{6 y}{6} = \frac{- 5 x}{6} + \frac{30}{6}$

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.

$\frac{6 y}{6} = \frac{- 5 x}{6} + \frac{30}{6}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 5 x}{6} + \frac{30}{6}$

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

Move the negative in front of the fraction.

$y = - \frac{5 x}{6} + \frac{30}{6}$

Step 1.3.3.1.2

Divide $30$ by $6$ .

$y = - \frac{5 x}{6} + 5$

Step 1.4

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

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Step 1.4.1

Reorder terms.

$y = - (\frac{5}{6} x) + 5$

Step 1.4.2

Remove parentheses.

$y = - \frac{5}{6} x + 5$

Step 2

Using the slope-intercept form, the slope is $- \frac{5}{6}$ .

$m = - \frac{5}{6}$

Step 3