Write in Slope-Intercept Form -x/5+(2y)/3=-6 1/6

$- \frac{x}{5} + \frac{2 y}{3} = - 6 \frac{1}{6}$

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Rewrite in slope-intercept form.

Simplify the right side.

Convert $6 \frac{1}{6}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$- \frac{x}{5} + \frac{2 y}{3} = - (6 + \frac{1}{6})$

Add $6$ and $\frac{1}{6}$ .

To write $6$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$- \frac{x}{5} + \frac{2 y}{3} = - (6 \cdot \frac{6}{6} + \frac{1}{6})$

Combine $6$ and $\frac{6}{6}$ .

$- \frac{x}{5} + \frac{2 y}{3} = - (\frac{6 \cdot 6}{6} + \frac{1}{6})$

Combine the numerators over the common denominator.

$- \frac{x}{5} + \frac{2 y}{3} = - \frac{6 \cdot 6 + 1}{6}$

Simplify the numerator.

Multiply $6$ by $6$ .

$- \frac{x}{5} + \frac{2 y}{3} = - \frac{36 + 1}{6}$

Add $36$ and $1$ .

$- \frac{x}{5} + \frac{2 y}{3} = - \frac{37}{6}$

Add $\frac{x}{5}$ to both sides of the equation.

$\frac{2 y}{3} = - \frac{37}{6} + \frac{x}{5}$

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} \cdot \frac{2 y}{3} = \frac{3}{2} (- \frac{37}{6} + \frac{x}{5})$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{3}{2} \cdot \frac{2 y}{3}$ .

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3}{2} \cdot \frac{2 y}{3} = \frac{3}{2} (- \frac{37}{6} + \frac{x}{5})$

Rewrite the expression.

$\frac{1}{2} (2 y) = \frac{3}{2} (- \frac{37}{6} + \frac{x}{5})$

Cancel the common factor of $2$ .

Factor $2$ out of $2 y$ .

$\frac{1}{2} (2 (y)) = \frac{3}{2} (- \frac{37}{6} + \frac{x}{5})$

Cancel the common factor.

$\frac{1}{2} (2 y) = \frac{3}{2} (- \frac{37}{6} + \frac{x}{5})$

Rewrite the expression.

$y = \frac{3}{2} (- \frac{37}{6} + \frac{x}{5})$

Simplify the right side.

Simplify $\frac{3}{2} (- \frac{37}{6} + \frac{x}{5})$ .

Apply the distributive property.

$y = \frac{3}{2} (- \frac{37}{6}) + \frac{3}{2} \cdot \frac{x}{5}$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{37}{6}$ into the numerator.

$y = \frac{3}{2} \cdot \frac{- 37}{6} + \frac{3}{2} \cdot \frac{x}{5}$

Factor $3$ out of $6$ .

$y = \frac{3}{2} \cdot \frac{- 37}{3 (2)} + \frac{3}{2} \cdot \frac{x}{5}$

Cancel the common factor.

$y = \frac{3}{2} \cdot \frac{- 37}{3 \cdot 2} + \frac{3}{2} \cdot \frac{x}{5}$

Rewrite the expression.

$y = \frac{1}{2} \cdot \frac{- 37}{2} + \frac{3}{2} \cdot \frac{x}{5}$

Multiply $\frac{1}{2}$ by $\frac{- 37}{2}$ .

$y = \frac{- 37}{2 \cdot 2} + \frac{3}{2} \cdot \frac{x}{5}$

Multiply $2$ by $2$ .

$y = \frac{- 37}{4} + \frac{3}{2} \cdot \frac{x}{5}$

Multiply $\frac{3}{2} \cdot \frac{x}{5}$ .

Multiply $\frac{3}{2}$ by $\frac{x}{5}$ .

$y = \frac{- 37}{4} + \frac{3 x}{2 \cdot 5}$

Multiply $2$ by $5$ .

$y = \frac{- 37}{4} + \frac{3 x}{10}$

Move the negative in front of the fraction.

$y = - \frac{37}{4} + \frac{3 x}{10}$

Reorder $- \frac{37}{4}$ and $\frac{3 x}{10}$ .

$y = \frac{3 x}{10} - \frac{37}{4}$

Reorder terms.

$y = \frac{3}{10} x - \frac{37}{4}$

Write in Slope-Intercept Form -x/5+(2y)/3=-6 1/6

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