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

$- 3 x + 5 y = 2 x + 3 y$

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.

$y = m x + b$

Move all terms containing $y$ to the left side of the equation.

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

$- 3 x + 5 y - 3 y = 2 x$

Subtract $3 y$ from $5 y$ .

$- 3 x + 2 y = 2 x$

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

Add $3 x$ to both sides of the equation.

$2 y = 2 x + 3 x$

Add $2 x$ and $3 x$ .

$2 y = 5 x$

Divide each term in $2 y = 5 x$ by $2$ and simplify.

Divide each term in $2 y = 5 x$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Reorder terms.

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

Step 2

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

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

$m = \frac{5}{2}$

$b = 0$

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

Slope: $\frac{5}{2}$

y-intercept: $(0, 0)$

Slope: $\frac{5}{2}$

y-intercept: $(0, 0)$

Step 3