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

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

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.

Multiply both sides by $2$ .

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

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Solve for $y$ .

Simplify $\frac{x - 3}{2}$ .

Split the fraction $\frac{x - 3}{2}$ into two fractions.

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

Move the negative in front of the fraction.

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

Subtract $x$ from both sides of the equation.

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

Divide each term in $- 4 y = \frac{x}{2} - \frac{3}{2} - x$ by $- 4$ and simplify.

Divide each term in $- 4 y = \frac{x}{2} - \frac{3}{2} - x$ by $- 4$ .

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

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Multiply the numerator by the reciprocal of the denominator.

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

Move the negative in front of the fraction.

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

Multiply $\frac{x}{2} (- \frac{1}{4})$ .

Multiply $\frac{x}{2}$ by $\frac{1}{4}$ .

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

Multiply $2$ by $4$ .

$y = - \frac{x}{8} + \frac{- \frac{3}{2}}{- 4} + \frac{- x}{- 4}$

Multiply the numerator by the reciprocal of the denominator.

$y = - \frac{x}{8} - \frac{3}{2} \cdot \frac{1}{- 4} + \frac{- x}{- 4}$

Move the negative in front of the fraction.

$y = - \frac{x}{8} - \frac{3}{2} (- \frac{1}{4}) + \frac{- x}{- 4}$

Multiply $- \frac{3}{2} (- \frac{1}{4})$ .

Multiply $- 1$ by $- 1$ .

$y = - \frac{x}{8} + 1 (\frac{3}{2}) \frac{1}{4} + \frac{- x}{- 4}$

Multiply $\frac{3}{2}$ by $1$ .

$y = - \frac{x}{8} + \frac{3}{2} \cdot \frac{1}{4} + \frac{- x}{- 4}$

Multiply $\frac{3}{2}$ by $\frac{1}{4}$ .

$y = - \frac{x}{8} + \frac{3}{2 \cdot 4} + \frac{- x}{- 4}$

Multiply $2$ by $4$ .

$y = - \frac{x}{8} + \frac{3}{8} + \frac{- x}{- 4}$

Dividing two negative values results in a positive value.

$y = - \frac{x}{8} + \frac{3}{8} + \frac{x}{4}$

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

Simplify $- \frac{x}{8} + \frac{3}{8} + \frac{x}{4}$ .

To write $\frac{x}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = - \frac{x}{8} + \frac{x}{4} \cdot \frac{2}{2} + \frac{3}{8}$

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x}{4}$ by $\frac{2}{2}$ .

$y = - \frac{x}{8} + \frac{x \cdot 2}{4 \cdot 2} + \frac{3}{8}$

Multiply $4$ by $2$ .

$y = - \frac{x}{8} + \frac{x \cdot 2}{8} + \frac{3}{8}$

Simplify terms.

Combine the numerators over the common denominator.

$y = \frac{- x + x \cdot 2}{8} + \frac{3}{8}$

Combine the numerators over the common denominator.

$y = \frac{- x + x \cdot 2 + 3}{8}$

Move $2$ to the left of $x$ .

$y = \frac{- x + 2 x + 3}{8}$

Add $- x$ and $2 x$ .

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

Split the fraction $\frac{x + 3}{8}$ into two fractions.

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

Reorder terms.

$y = \frac{1}{8} x + \frac{3}{8}$

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

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