Find the Slope and y-intercept -2(4x+3)=3(3y+4)

$- 2 (4 x + 3) = 3 (3 y + 4)$

Step 1

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.

$y = m x + b$

Simplify the left side.

Simplify $- 2 (4 x + 3)$ .

Apply the distributive property.

$- 2 (4 x) - 2 \cdot 3 = 3 (3 y + 4)$

Multiply.

Multiply $4$ by $- 2$ .

$- 8 x - 2 \cdot 3 = 3 (3 y + 4)$

Multiply $- 2$ by $3$ .

$- 8 x - 6 = 3 (3 y + 4)$

Simplify the right side.

Simplify $3 (3 y + 4)$ .

Apply the distributive property.

$- 8 x - 6 = 3 (3 y) + 3 \cdot 4$

Multiply.

Multiply $3$ by $3$ .

$- 8 x - 6 = 9 y + 3 \cdot 4$

Multiply $3$ by $4$ .

$- 8 x - 6 = 9 y + 12$

Rewrite the equation as $9 y + 12 = - 8 x - 6$ .

$9 y + 12 = - 8 x - 6$

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

Subtract $12$ from both sides of the equation.

$9 y = - 8 x - 6 - 12$

Subtract $12$ from $- 6$ .

$9 y = - 8 x - 18$

Divide each term in $9 y = - 8 x - 18$ by $9$ and simplify.

Divide each term in $9 y = - 8 x - 18$ by $9$ .

$\frac{9 y}{9} = \frac{- 8 x}{9} + \frac{- 18}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 y}{9} = \frac{- 8 x}{9} + \frac{- 18}{9}$

Divide $y$ by $1$ .

$y = \frac{- 8 x}{9} + \frac{- 18}{9}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{(8) x}{9} + \frac{- 18}{9}$

Divide $- 18$ by $9$ .

$y = - \frac{8 x}{9} - 2$

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

Reorder terms.

$y = - (\frac{8}{9} x) - 2$

Remove parentheses.

$y = - \frac{8}{9} x - 2$

Step 2

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

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

$m = - \frac{8}{9}$

$b = - 2$

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

Slope: $- \frac{8}{9}$

y-intercept: $(0, - 2)$

Slope: $- \frac{8}{9}$

y-intercept: $(0, - 2)$

Step 3

Find the Slope and y-intercept -2(4x+3)=3(3y+4)

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