Write in y=mx+b Form (5x-4y)/3=(3x-2)/6

$\frac{5 x - 4 y}{3} = \frac{3 x - 2}{6}$

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.

Multiply both sides by $3$ .

$\frac{5 x - 4 y}{3} \cdot 3 = \frac{3 x - 2}{6} \cdot 3$

Simplify.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{5 x - 4 y}{3} \cdot 3 = \frac{3 x - 2}{6} \cdot 3$

Rewrite the expression.

$5 x - 4 y = \frac{3 x - 2}{6} \cdot 3$

Simplify the right side.

Cancel the common factor of $3$ .

Factor $3$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Solve for $y$ .

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

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

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

Divide $- 2$ by $2$ .

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

Subtract $5 x$ from both sides of the equation.

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

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

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

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

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Multiply the numerator by the reciprocal of the denominator.

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

Move the negative in front of the fraction.

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

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

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

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

Multiply $2$ by $4$ .

$y = - \frac{3 x}{8} + \frac{- 1}{- 4} + \frac{- 5 x}{- 4}$

Dividing two negative values results in a positive value.

$y = - \frac{3 x}{8} + \frac{1}{4} + \frac{- 5 x}{- 4}$

Dividing two negative values results in a positive value.

$y = - \frac{3 x}{8} + \frac{1}{4} + \frac{5 x}{4}$

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

Simplify $- \frac{3 x}{8} + \frac{1}{4} + \frac{5 x}{4}$ .

To write $\frac{5 x}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = - \frac{3 x}{8} + \frac{5 x}{4} \cdot \frac{2}{2} + \frac{1}{4}$

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

Multiply $\frac{5 x}{4}$ by $\frac{2}{2}$ .

$y = - \frac{3 x}{8} + \frac{5 x \cdot 2}{4 \cdot 2} + \frac{1}{4}$

Multiply $4$ by $2$ .

$y = - \frac{3 x}{8} + \frac{5 x \cdot 2}{8} + \frac{1}{4}$

Combine the numerators over the common denominator.

$y = \frac{- 3 x + 5 x \cdot 2}{8} + \frac{1}{4}$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $- 3 x + 5 x \cdot 2$ .

Factor $x$ out of $- 3 x$ .

$y = \frac{x \cdot - 3 + 5 x \cdot 2}{8} + \frac{1}{4}$

Factor $x$ out of $5 x \cdot 2$ .

$y = \frac{x \cdot - 3 + x (5 \cdot 2)}{8} + \frac{1}{4}$

Factor $x$ out of $x \cdot - 3 + x (5 \cdot 2)$ .

$y = \frac{x (- 3 + 5 \cdot 2)}{8} + \frac{1}{4}$

Multiply $5$ by $2$ .

$y = \frac{x (- 3 + 10)}{8} + \frac{1}{4}$

Add $- 3$ and $10$ .

$y = \frac{x \cdot 7}{8} + \frac{1}{4}$

Move $7$ to the left of $x$ .

$y = \frac{7 x}{8} + \frac{1}{4}$

Reorder terms.

$y = \frac{7}{8} x + \frac{1}{4}$

Write in y=mx+b Form (5x-4y)/3=(3x-2)/6

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