Write in y=mx+b Form 3x-4y=6

$3 x - 4 y = 6$

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.

Subtract $3 x$ from both sides of the equation.

$- 4 y = 6 - 3 x$

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

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

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

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

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

Factor $2$ out of $6$ .

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

Cancel the common factors.

Factor $2$ out of $- 4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Dividing two negative values results in a positive value.

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

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

Reorder $- \frac{3}{2}$ and $\frac{3 x}{4}$ .

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

Reorder terms.

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