Write in y=mx+b Form 6-(5y-6x)/2=5x+5

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

Step 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 2

Rewrite in slope-intercept form.

Simplify the left side.

Simplify $6 - \frac{5 y - 6 x}{2}$ .

To write $6$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Simplify terms.

Combine $6$ and $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $6$ by $2$ .

$\frac{12 - (5 y - 6 x)}{2} = 5 x + 5$

Apply the distributive property.

$\frac{12 - (5 y) - (- 6 x)}{2} = 5 x + 5$

Multiply $5$ by $- 1$ .

$\frac{12 - 5 y - (- 6 x)}{2} = 5 x + 5$

Multiply $- 6$ by $- 1$ .

$\frac{12 - 5 y + 6 x}{2} = 5 x + 5$

Multiply both sides by $2$ .

$\frac{12 - 5 y + 6 x}{2} \cdot 2 = (5 x + 5) \cdot 2$

Simplify.

Simplify the left side.

Simplify $\frac{12 - 5 y + 6 x}{2} \cdot 2$ .

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{12 - 5 y + 6 x}{2} \cdot 2 = (5 x + 5) \cdot 2$

Rewrite the expression.

$12 - 5 y + 6 x = (5 x + 5) \cdot 2$

Simplify the expression.

Move $12$ .

$- 5 y + 6 x + 12 = (5 x + 5) \cdot 2$

Reorder $- 5 y$ and $6 x$ .

$6 x - 5 y + 12 = (5 x + 5) \cdot 2$

Simplify the right side.

Simplify $(5 x + 5) \cdot 2$ .

Apply the distributive property.

$6 x - 5 y + 12 = 5 x \cdot 2 + 5 \cdot 2$

Multiply.

Multiply $2$ by $5$ .

$6 x - 5 y + 12 = 10 x + 5 \cdot 2$

Multiply $5$ by $2$ .

$6 x - 5 y + 12 = 10 x + 10$

Solve for $y$ .

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

Subtract $6 x$ from both sides of the equation.

$- 5 y + 12 = 10 x + 10 - 6 x$

Subtract $12$ from both sides of the equation.

$- 5 y = 10 x + 10 - 6 x - 12$

Subtract $6 x$ from $10 x$ .

$- 5 y = 4 x + 10 - 12$

Subtract $12$ from $10$ .

$- 5 y = 4 x - 2$

Divide each term in $- 5 y = 4 x - 2$ by $- 5$ and simplify.

Divide each term in $- 5 y = 4 x - 2$ by $- 5$ .

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

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

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

Dividing two negative values results in a positive value.

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

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

Reorder terms.

$y = - (\frac{4}{5} x) + \frac{2}{5}$

Remove parentheses.

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

Write in y=mx+b Form 6-(5y-6x)/2=5x+5

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