Write in y=mx+b Form 6-(3y-6x)/2=7x+1

$6 - \frac{3 y - 6 x}{2} = 7 x + 1$

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 $6 - \frac{3 y - 6 x}{2}$ .

Factor $3$ out of $3 y - 6 x$ .

Factor $3$ out of $3 y$ .

$6 - \frac{3 (y) - 6 x}{2} = 7 x + 1$

Factor $3$ out of $- 6 x$ .

$6 - \frac{3 (y) + 3 (- 2 x)}{2} = 7 x + 1$

Factor $3$ out of $3 (y) + 3 (- 2 x)$ .

$6 - \frac{3 (y - 2 x)}{2} = 7 x + 1$

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

$6 \cdot \frac{2}{2} - \frac{3 (y - 2 x)}{2} = 7 x + 1$

Simplify terms.

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

$\frac{6 \cdot 2}{2} - \frac{3 (y - 2 x)}{2} = 7 x + 1$

Combine the numerators over the common denominator.

$\frac{6 \cdot 2 - 3 (y - 2 x)}{2} = 7 x + 1$

Simplify the numerator.

Factor $3$ out of $6 \cdot 2 - 3 (y - 2 x)$ .

Factor $3$ out of $6 \cdot 2$ .

$\frac{3 (2 \cdot 2) - 3 (y - 2 x)}{2} = 7 x + 1$

Factor $3$ out of $- 3 (y - 2 x)$ .

$\frac{3 (2 \cdot 2) + 3 (- (y - 2 x))}{2} = 7 x + 1$

Factor $3$ out of $3 (2 \cdot 2) + 3 (- (y - 2 x))$ .

$\frac{3 (2 \cdot 2 - (y - 2 x))}{2} = 7 x + 1$

Multiply $2$ by $2$ .

$\frac{3 (4 - (y - 2 x))}{2} = 7 x + 1$

Apply the distributive property.

$\frac{3 (4 - y - (- 2 x))}{2} = 7 x + 1$

Multiply $- 2$ by $- 1$ .

$\frac{3 (4 - y + 2 x)}{2} = 7 x + 1$

Multiply both sides by $2$ .

$\frac{3 (4 - y + 2 x)}{2} \cdot 2 = (7 x + 1) \cdot 2$

Simplify.

Simplify the left side.

Simplify $\frac{3 (4 - y + 2 x)}{2} \cdot 2$ .

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{3 (4 - y + 2 x)}{2} \cdot 2 = (7 x + 1) \cdot 2$

Rewrite the expression.

$3 (4 - y + 2 x) = (7 x + 1) \cdot 2$

Apply the distributive property.

$3 \cdot 4 + 3 (- y) + 3 (2 x) = (7 x + 1) \cdot 2$

Simplify.

Multiply $3$ by $4$ .

$12 + 3 (- y) + 3 (2 x) = (7 x + 1) \cdot 2$

Multiply $- 1$ by $3$ .

$12 - 3 y + 3 (2 x) = (7 x + 1) \cdot 2$

Multiply $2$ by $3$ .

$12 - 3 y + 6 x = (7 x + 1) \cdot 2$

Move $12$ .

$- 3 y + 6 x + 12 = (7 x + 1) \cdot 2$

Reorder $- 3 y$ and $6 x$ .

$6 x - 3 y + 12 = (7 x + 1) \cdot 2$

Simplify the right side.

Simplify $(7 x + 1) \cdot 2$ .

Apply the distributive property.

$6 x - 3 y + 12 = 7 x \cdot 2 + 1 \cdot 2$

Multiply.

Multiply $2$ by $7$ .

$6 x - 3 y + 12 = 14 x + 1 \cdot 2$

Multiply $2$ by $1$ .

$6 x - 3 y + 12 = 14 x + 2$

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.

$- 3 y + 12 = 14 x + 2 - 6 x$

Subtract $12$ from both sides of the equation.

$- 3 y = 14 x + 2 - 6 x - 12$

Subtract $6 x$ from $14 x$ .

$- 3 y = 8 x + 2 - 12$

Subtract $12$ from $2$ .

$- 3 y = 8 x - 10$

Divide each term in $- 3 y = 8 x - 10$ by $- 3$ and simplify.

Divide each term in $- 3 y = 8 x - 10$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{8 x}{- 3} + \frac{- 10}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{8 x}{- 3} + \frac{- 10}{- 3}$

Divide $y$ by $1$ .

$y = \frac{8 x}{- 3} + \frac{- 10}{- 3}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{8 x}{3} + \frac{- 10}{- 3}$

Dividing two negative values results in a positive value.

$y = - \frac{8 x}{3} + \frac{10}{3}$

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

Reorder terms.

$y = - (\frac{8}{3} x) + \frac{10}{3}$

Remove parentheses.

$y = - \frac{8}{3} x + \frac{10}{3}$

Write in y=mx+b Form 6-(3y-6x)/2=7x+1

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