Find the Slope and y-intercept 3x+2y=2x+8

$3 x + 2 y = 2 x + 8$

Rewrite in slope-intercept form.

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Move all terms not containing $y$ to the right side of the equation.

Subtract $3 x$ from both sides of the equation.

$2 y = 2 x + 8 - 3 x$

Subtract $3 x$ from $2 x$ .

$2 y = - x + 8$

Divide each term in $2 y = - x + 8$ by $2$ and simplify.

Divide each term in $2 y = - x + 8$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

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

Divide $8$ by $2$ .

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

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

Reorder terms.

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

Remove parentheses.

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

Use the slope-intercept form to find the slope and y-intercept.

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = - \frac{1}{2}$

$b = 4$

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $- \frac{1}{2}$

y-intercept: $(0, 4)$

Slope: $- \frac{1}{2}$

y-intercept: $(0, 4)$