Write in y=mx+b Form 3-(6y+3x)/2=5

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

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

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

Factor $3$ out of $6 y$ .

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

Factor $3$ out of $3 x$ .

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

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

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

To write $3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Simplify terms.

Combine $3$ and $\frac{2}{2}$ .

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

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

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

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

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

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

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

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

Apply the distributive property.

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

Multiply $2$ by $- 1$ .

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

Multiply both sides by $2$ .

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

Simplify.

Simplify the left side.

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$3 (2 - 2 y - x) = 5 \cdot 2$

Apply the distributive property.

$3 \cdot 2 + 3 (- 2 y) + 3 (- x) = 5 \cdot 2$

Simplify.

Multiply $3$ by $2$ .

$6 + 3 (- 2 y) + 3 (- x) = 5 \cdot 2$

Multiply $- 2$ by $3$ .

$6 - 6 y + 3 (- x) = 5 \cdot 2$

Multiply $- 1$ by $3$ .

$6 - 6 y - 3 x = 5 \cdot 2$

Move $6$ .

$- 6 y - 3 x + 6 = 5 \cdot 2$

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

$- 3 x - 6 y + 6 = 5 \cdot 2$

Simplify the right side.

Multiply $5$ by $2$ .

$- 3 x - 6 y + 6 = 10$

Solve for $y$ .

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

Add $3 x$ to both sides of the equation.

$- 6 y + 6 = 10 + 3 x$

Subtract $6$ from both sides of the equation.

$- 6 y = 10 + 3 x - 6$

Subtract $6$ from $10$ .

$- 6 y = 3 x + 4$

Divide each term in $- 6 y = 3 x + 4$ by $- 6$ and simplify.

Divide each term in $- 6 y = 3 x + 4$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{3 x}{- 6} + \frac{4}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{3 x}{- 6} + \frac{4}{- 6}$

Divide $y$ by $1$ .

$y = \frac{3 x}{- 6} + \frac{4}{- 6}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $3$ and $- 6$ .

Factor $3$ out of $3 x$ .

$y = \frac{3 (x)}{- 6} + \frac{4}{- 6}$

Cancel the common factors.

Factor $3$ out of $- 6$ .

$y = \frac{3 x}{3 \cdot - 2} + \frac{4}{- 6}$

Cancel the common factor.

$y = \frac{3 x}{3 \cdot - 2} + \frac{4}{- 6}$

Rewrite the expression.

$y = \frac{x}{- 2} + \frac{4}{- 6}$

Move the negative in front of the fraction.

$y = - \frac{x}{2} + \frac{4}{- 6}$

Cancel the common factor of $4$ and $- 6$ .

Factor $2$ out of $4$ .

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

Cancel the common factors.

Factor $2$ out of $- 6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

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

Reorder terms.

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

Remove parentheses.

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

Write in y=mx+b Form 3-(6y+3x)/2=5

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