Write in y=mx+b Form 7x+5y=2y-5

$7 x + 5 y = 2 y - 5$

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.

Move all terms containing $y$ to the left side of the equation.

Subtract $2 y$ from both sides of the equation.

$7 x + 5 y - 2 y = - 5$

Subtract $2 y$ from $5 y$ .

$7 x + 3 y = - 5$

Subtract $7 x$ from both sides of the equation.

$3 y = - 5 - 7 x$

Divide each term in $3 y = - 5 - 7 x$ by $3$ and simplify.

Divide each term in $3 y = - 5 - 7 x$ by $3$ .

$\frac{3 y}{3} = \frac{- 5}{3} + \frac{- 7 x}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 y}{3} = \frac{- 5}{3} + \frac{- 7 x}{3}$

Divide $y$ by $1$ .

$y = \frac{- 5}{3} + \frac{- 7 x}{3}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{5}{3} + \frac{- 7 x}{3}$

Move the negative in front of the fraction.

$y = - \frac{5}{3} - \frac{7 x}{3}$

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

Reorder $- \frac{5}{3}$ and $- \frac{7 x}{3}$ .

$y = - \frac{7 x}{3} - \frac{5}{3}$

Reorder terms.

$y = - (\frac{7}{3} x) - \frac{5}{3}$

Remove parentheses.

$y = - \frac{7}{3} x - \frac{5}{3}$