Find the Slope and y-intercept 6x+7y=4x+4y

$6 x + 7 y = 4 x + 4 y$

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 containing $y$ to the left side of the equation.

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

$6 x + 7 y - 4 y = 4 x$

Subtract $4 y$ from $7 y$ .

$6 x + 3 y = 4 x$

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

Subtract $6 x$ from both sides of the equation.

$3 y = 4 x - 6 x$

Subtract $6 x$ from $4 x$ .

$3 y = - 2 x$

Divide each term in $3 y = - 2 x$ by $3$ and simplify.

Divide each term in $3 y = - 2 x$ by $3$ .

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

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

Reorder terms.

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

Remove parentheses.

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

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

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

$m = - \frac{2}{3}$

$b = 0$

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

Slope: $- \frac{2}{3}$

y-intercept: $(0, 0)$

Slope: $- \frac{2}{3}$

y-intercept: $(0, 0)$