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

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

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 $2$ .

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

Simplify.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the right side.

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Solve for $y$ .

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

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

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

Move the negative in front of the fraction.

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

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

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

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

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

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

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Multiply the numerator by the reciprocal of the denominator.

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

Move the negative in front of the fraction.

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

Multiply $\frac{x}{2} (- \frac{1}{5})$ .

Multiply $\frac{x}{2}$ by $\frac{1}{5}$ .

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

Multiply $2$ by $5$ .

$y = - \frac{x}{10} + \frac{- \frac{5}{2}}{- 5} + \frac{- 4 x}{- 5}$

Multiply the numerator by the reciprocal of the denominator.

$y = - \frac{x}{10} - \frac{5}{2} \cdot \frac{1}{- 5} + \frac{- 4 x}{- 5}$

Cancel the common factor of $5$ .

Move the leading negative in $- \frac{5}{2}$ into the numerator.

$y = - \frac{x}{10} + \frac{- 5}{2} \cdot \frac{1}{- 5} + \frac{- 4 x}{- 5}$

Factor $5$ out of $- 5$ .

$y = - \frac{x}{10} + \frac{5 (- 1)}{2} \cdot \frac{1}{- 5} + \frac{- 4 x}{- 5}$

Factor $5$ out of $- 5$ .

$y = - \frac{x}{10} + \frac{5 \cdot - 1}{2} \cdot \frac{1}{5 \cdot - 1} + \frac{- 4 x}{- 5}$

Cancel the common factor.

$y = - \frac{x}{10} + \frac{5 \cdot - 1}{2} \cdot \frac{1}{5 \cdot - 1} + \frac{- 4 x}{- 5}$

Rewrite the expression.

$y = - \frac{x}{10} + \frac{- 1}{2} \cdot \frac{1}{- 1} + \frac{- 4 x}{- 5}$

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

$y = - \frac{x}{10} + \frac{- 1}{2 \cdot - 1} + \frac{- 4 x}{- 5}$

Multiply $2$ by $- 1$ .

$y = - \frac{x}{10} + \frac{- 1}{- 2} + \frac{- 4 x}{- 5}$

Dividing two negative values results in a positive value.

$y = - \frac{x}{10} + \frac{1}{2} + \frac{- 4 x}{- 5}$

Dividing two negative values results in a positive value.

$y = - \frac{x}{10} + \frac{1}{2} + \frac{4 x}{5}$

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

Simplify $- \frac{x}{10} + \frac{1}{2} + \frac{4 x}{5}$ .

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

$y = - \frac{x}{10} + \frac{4 x}{5} \cdot \frac{2}{2} + \frac{1}{2}$

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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

$y = - \frac{x}{10} + \frac{4 x \cdot 2}{5 \cdot 2} + \frac{1}{2}$

Multiply $5$ by $2$ .

$y = - \frac{x}{10} + \frac{4 x \cdot 2}{10} + \frac{1}{2}$

Combine the numerators over the common denominator.

$y = \frac{- x + 4 x \cdot 2}{10} + \frac{1}{2}$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $- x + 4 x \cdot 2$ .

Factor $x$ out of $- x$ .

$y = \frac{x \cdot - 1 + 4 x \cdot 2}{10} + \frac{1}{2}$

Factor $x$ out of $4 x \cdot 2$ .

$y = \frac{x \cdot - 1 + x (4 \cdot 2)}{10} + \frac{1}{2}$

Factor $x$ out of $x \cdot - 1 + x (4 \cdot 2)$ .

$y = \frac{x (- 1 + 4 \cdot 2)}{10} + \frac{1}{2}$

Multiply $4$ by $2$ .

$y = \frac{x (- 1 + 8)}{10} + \frac{1}{2}$

Add $- 1$ and $8$ .

$y = \frac{x \cdot 7}{10} + \frac{1}{2}$

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

$y = \frac{7 x}{10} + \frac{1}{2}$

Reorder terms.

$y = \frac{7}{10} x + \frac{1}{2}$

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

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