Find the Slope and y-intercept -6x+15y+45=0

$- 6 x + 15 y + 45 = 0$

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 not containing $y$ to the right side of the equation.

Add $6 x$ to both sides of the equation.

$15 y + 45 = 6 x$

Subtract $45$ from both sides of the equation.

$15 y = 6 x - 45$

Divide each term in $15 y = 6 x - 45$ by $15$ and simplify.

Divide each term in $15 y = 6 x - 45$ by $15$ .

$\frac{15 y}{15} = \frac{6 x}{15} + \frac{- 45}{15}$

Simplify the left side.

Cancel the common factor of $15$ .

Cancel the common factor.

$\frac{15 y}{15} = \frac{6 x}{15} + \frac{- 45}{15}$

Divide $y$ by $1$ .

$y = \frac{6 x}{15} + \frac{- 45}{15}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $6$ and $15$ .

Factor $3$ out of $6 x$ .

$y = \frac{3 (2 x)}{15} + \frac{- 45}{15}$

Cancel the common factors.

Factor $3$ out of $15$ .

$y = \frac{3 (2 x)}{3 (5)} + \frac{- 45}{15}$

Cancel the common factor.

$y = \frac{3 (2 x)}{3 \cdot 5} + \frac{- 45}{15}$

Rewrite the expression.

$y = \frac{2 x}{5} + \frac{- 45}{15}$

Divide $- 45$ by $15$ .

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

Reorder terms.

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

Step 2

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

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

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

$b = - 3$

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

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

y-intercept: $(0, - 3)$

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

y-intercept: $(0, - 3)$

Step 3

Find the Slope and y-intercept -6x+15y+45=0

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