Write in y=mx+b Form (4x-y)/2=(5x-3)/4

$\frac{4 x - y}{2} = \frac{5 x - 3}{4}$

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 $2$ .

$\frac{4 x - y}{2} \cdot 2 = \frac{5 x - 3}{4} \cdot 2$

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{4 x - y}{2} \cdot 2 = \frac{5 x - 3}{4} \cdot 2$

Rewrite the expression.

$4 x - y = \frac{5 x - 3}{4} \cdot 2$

Simplify the right side.

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$4 x - y = \frac{5 x - 3}{2 (2)} \cdot 2$

Cancel the common factor.

$4 x - y = \frac{5 x - 3}{2 \cdot 2} \cdot 2$

Rewrite the expression.

$4 x - y = \frac{5 x - 3}{2}$

Solve for $y$ .

Simplify $\frac{5 x - 3}{2}$ .

Split the fraction $\frac{5 x - 3}{2}$ into two fractions.

$4 x - y = \frac{5 x}{2} + \frac{- 3}{2}$

Move the negative in front of the fraction.

$4 x - y = \frac{5 x}{2} - \frac{3}{2}$

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

$- y = \frac{5 x}{2} - \frac{3}{2} - 4 x$

Divide each term in $- y = \frac{5 x}{2} - \frac{3}{2} - 4 x$ by $- 1$ and simplify.

Divide each term in $- y = \frac{5 x}{2} - \frac{3}{2} - 4 x$ by $- 1$ .

$\frac{- y}{- 1} = \frac{\frac{5 x}{2}}{- 1} + \frac{- \frac{3}{2}}{- 1} + \frac{- 4 x}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{\frac{5 x}{2}}{- 1} + \frac{- \frac{3}{2}}{- 1} + \frac{- 4 x}{- 1}$

Divide $y$ by $1$ .

$y = \frac{\frac{5 x}{2}}{- 1} + \frac{- \frac{3}{2}}{- 1} + \frac{- 4 x}{- 1}$

Simplify the right side.

Simplify each term.

Move the negative one from the denominator of $\frac{\frac{5 x}{2}}{- 1}$ .

$y = - 1 \cdot \frac{5 x}{2} + \frac{- \frac{3}{2}}{- 1} + \frac{- 4 x}{- 1}$

Rewrite $- 1 \cdot \frac{5 x}{2}$ as $- \frac{5 x}{2}$ .

$y = - \frac{5 x}{2} + \frac{- \frac{3}{2}}{- 1} + \frac{- 4 x}{- 1}$

Dividing two negative values results in a positive value.

$y = - \frac{5 x}{2} + \frac{\frac{3}{2}}{1} + \frac{- 4 x}{- 1}$

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

$y = - \frac{5 x}{2} + \frac{3}{2} + \frac{- 4 x}{- 1}$

Move the negative one from the denominator of $\frac{- 4 x}{- 1}$ .

$y = - \frac{5 x}{2} + \frac{3}{2} - 1 \cdot (- 4 x)$

Rewrite $- 1 \cdot (- 4 x)$ as $- (- 4 x)$ .

$y = - \frac{5 x}{2} + \frac{3}{2} - (- 4 x)$

Multiply $- 4$ by $- 1$ .

$y = - \frac{5 x}{2} + \frac{3}{2} + 4 x$

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

Simplify $- \frac{5 x}{2} + \frac{3}{2} + 4 x$ .

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

$y = - \frac{5 x}{2} + 4 x \cdot \frac{2}{2} + \frac{3}{2}$

Combine $4 x$ and $\frac{2}{2}$ .

$y = - \frac{5 x}{2} + \frac{4 x \cdot 2}{2} + \frac{3}{2}$

Combine the numerators over the common denominator.

$y = \frac{- 5 x + 4 x \cdot 2}{2} + \frac{3}{2}$

Combine the numerators over the common denominator.

$y = \frac{- 5 x + 4 x \cdot 2 + 3}{2}$

Multiply $2$ by $4$ .

$y = \frac{- 5 x + 8 x + 3}{2}$

Add $- 5 x$ and $8 x$ .

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

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

Factor $3$ out of $3 x$ .

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

Factor $3$ out of $3$ .

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

Factor $3$ out of $3 (x) + 3 (1)$ .

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

Apply the distributive property.

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

Multiply $3$ by $1$ .

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

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

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

Reorder terms.

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

Write in y=mx+b Form (4x-y)/2=(5x-3)/4

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