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

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

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.

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

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Combine into one fraction.

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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.

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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 of the equation by $2$ .

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

Remove parentheses.

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

Simplify each term.

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Multiply $2$ by $7$ .

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

Multiply $3$ by $2$ .

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

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

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Subtract $2$ from both sides of the equation.

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

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

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

Subtract $4 x$ from $14 x$ .

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

Subtract $2$ from $6$ .

$- 3 y = 10 x + 4$

Divide each term by $- 3$ and simplify.

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

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

Cancel the common factor of $- 3$ .

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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 each term.

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Move the negative in front of the fraction.

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

Move the negative in front of the fraction.

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

Rewrite in slope-intercept form.

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

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