Find the Slope and y-intercept 2/3x=3/5y+2

$\frac{2}{3} x = \frac{3}{5} y + 2$

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.

Combine $\frac{2}{3}$ and $x$ .

$\frac{2 x}{3} = \frac{3}{5} y + 2$

Simplify the right side.

Combine $\frac{3}{5}$ and $y$ .

$\frac{2 x}{3} = \frac{3 y}{5} + 2$

Rewrite the equation as $\frac{3 y}{5} + 2 = \frac{2 x}{3}$ .

$\frac{3 y}{5} + 2 = \frac{2 x}{3}$

Subtract $2$ from both sides of the equation.

$\frac{3 y}{5} = \frac{2 x}{3} - 2$

Multiply both sides of the equation by $\frac{5}{3}$ .

$\frac{5}{3} \cdot \frac{3 y}{5} = \frac{5}{3} (\frac{2 x}{3} - 2)$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{5}{3} \cdot \frac{3 y}{5}$ .

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5}{3} \cdot \frac{3 y}{5} = \frac{5}{3} (\frac{2 x}{3} - 2)$

Rewrite the expression.

$\frac{1}{3} (3 y) = \frac{5}{3} (\frac{2 x}{3} - 2)$

Cancel the common factor of $3$ .

Factor $3$ out of $3 y$ .

$\frac{1}{3} (3 (y)) = \frac{5}{3} (\frac{2 x}{3} - 2)$

Cancel the common factor.

$\frac{1}{3} (3 y) = \frac{5}{3} (\frac{2 x}{3} - 2)$

Rewrite the expression.

$y = \frac{5}{3} (\frac{2 x}{3} - 2)$

Simplify the right side.

Simplify $\frac{5}{3} (\frac{2 x}{3} - 2)$ .

Apply the distributive property.

$y = \frac{5}{3} \cdot \frac{2 x}{3} + \frac{5}{3} \cdot - 2$

Multiply $\frac{5}{3} \cdot \frac{2 x}{3}$ .

Multiply $\frac{5}{3}$ by $\frac{2 x}{3}$ .

$y = \frac{5 (2 x)}{3 \cdot 3} + \frac{5}{3} \cdot - 2$

Multiply $2$ by $5$ .

$y = \frac{10 x}{3 \cdot 3} + \frac{5}{3} \cdot - 2$

Multiply $3$ by $3$ .

$y = \frac{10 x}{9} + \frac{5}{3} \cdot - 2$

Multiply $\frac{5}{3} \cdot - 2$ .

Combine $\frac{5}{3}$ and $- 2$ .

$y = \frac{10 x}{9} + \frac{5 \cdot - 2}{3}$

Multiply $5$ by $- 2$ .

$y = \frac{10 x}{9} + \frac{- 10}{3}$

Move the negative in front of the fraction.

$y = \frac{10 x}{9} - \frac{10}{3}$

Reorder terms.

$y = \frac{10}{9} x - \frac{10}{3}$

Step 2

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

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

$m = \frac{10}{9}$

$b = - \frac{10}{3}$

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

Slope: $\frac{10}{9}$

y-intercept: $(0, - \frac{10}{3})$

Slope: $\frac{10}{9}$

y-intercept: $(0, - \frac{10}{3})$

Step 3

Find the Slope and y-intercept 2/3x=3/5y+2

Related Questions

Support LCMGCF.com by disabling your adblocker.