Write in y=mx+b Form 1-(3y-4x)/2=7x+3

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

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 $1 - \frac{3 y - 4 x}{2}$ .

Combine into one fraction.

Write $1$ as a fraction with a common denominator.

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Apply the distributive property.

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

Multiply $3$ by $- 1$ .

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

Multiply $- 4$ by $- 1$ .

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

Multiply both sides by $2$ .

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

Simplify.

Simplify the left side.

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the expression.

Move $2$ .

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

Reorder $- 3 y$ and $4 x$ .

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

Simplify the right side.

Simplify $(7 x + 3) \cdot 2$ .

Apply the distributive property.

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

Multiply.

Multiply $2$ by $7$ .

$4 x - 3 y + 2 = 14 x + 3 \cdot 2$

Multiply $3$ by $2$ .

$4 x - 3 y + 2 = 14 x + 6$

Solve for $y$ .

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

Subtract $4 x$ from both sides of the equation.

$- 3 y + 2 = 14 x + 6 - 4 x$

Subtract $2$ from both sides of the equation.

$- 3 y = 14 x + 6 - 4 x - 2$

Subtract $4 x$ from $14 x$ .

$- 3 y = 10 x + 6 - 2$

Subtract $2$ from $6$ .

$- 3 y = 10 x + 4$

Divide each term in $- 3 y = 10 x + 4$ by $- 3$ and simplify.

Divide each term in $- 3 y = 10 x + 4$ by $- 3$ .

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

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

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

Move the negative in front of the fraction.

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

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

Reorder terms.

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

Remove parentheses.

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

Write in y=mx+b Form 1-(3y-4x)/2=7x+3

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