Find the Slope and y-intercept 5(y+2)=4(x-3)

$5 (y + 2) = 4 (x - 3)$

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 $5 (y + 2)$ .

Apply the distributive property.

$5 y + 5 \cdot 2 = 4 (x - 3)$

Multiply $5$ by $2$ .

$5 y + 10 = 4 (x - 3)$

Simplify the right side.

Simplify $4 (x - 3)$ .

Apply the distributive property.

$5 y + 10 = 4 x + 4 \cdot - 3$

Multiply $4$ by $- 3$ .

$5 y + 10 = 4 x - 12$

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

Subtract $10$ from both sides of the equation.

$5 y = 4 x - 12 - 10$

Subtract $10$ from $- 12$ .

$5 y = 4 x - 22$

Divide each term in $5 y = 4 x - 22$ by $5$ and simplify.

Divide each term in $5 y = 4 x - 22$ by $5$ .

$\frac{5 y}{5} = \frac{4 x}{5} + \frac{- 22}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} = \frac{4 x}{5} + \frac{- 22}{5}$

Divide $y$ by $1$ .

$y = \frac{4 x}{5} + \frac{- 22}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$y = \frac{4 x}{5} - \frac{22}{5}$

Reorder terms.

$y = \frac{4}{5} x - \frac{22}{5}$

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

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

$m = \frac{4}{5}$

$b = - \frac{22}{5}$

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

Slope: $\frac{4}{5}$

y-intercept: $(0, - \frac{22}{5})$

Slope: $\frac{4}{5}$

y-intercept: $(0, - \frac{22}{5})$