Find the Slope and y-intercept -2x-6y=5

$- 2 x - 6 y = 5$

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.

$y = m x + b$

Add $2 x$ to both sides of the equation.

$- 6 y = 5 + 2 x$

Divide each term in $- 6 y = 5 + 2 x$ by $- 6$ and simplify.

Divide each term in $- 6 y = 5 + 2 x$ by $- 6$ .

$\frac{- 6 y}{- 6} = \frac{5}{- 6} + \frac{2 x}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 y}{- 6} = \frac{5}{- 6} + \frac{2 x}{- 6}$

Divide $y$ by $1$ .

$y = \frac{5}{- 6} + \frac{2 x}{- 6}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{5}{6} + \frac{2 x}{- 6}$

Cancel the common factor of $2$ and $- 6$ .

Factor $2$ out of $2 x$ .

$y = - \frac{5}{6} + \frac{2 (x)}{- 6}$

Cancel the common factors.

Factor $2$ out of $- 6$ .

$y = - \frac{5}{6} + \frac{2 x}{2 \cdot - 3}$

Cancel the common factor.

$y = - \frac{5}{6} + \frac{2 x}{2 \cdot - 3}$

Rewrite the expression.

$y = - \frac{5}{6} + \frac{x}{- 3}$

Move the negative in front of the fraction.

$y = - \frac{5}{6} - \frac{x}{3}$

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

Reorder $- \frac{5}{6}$ and $- \frac{x}{3}$ .

$y = - \frac{x}{3} - \frac{5}{6}$

Reorder terms.

$y = - (\frac{1}{3} x) - \frac{5}{6}$

Remove parentheses.

$y = - \frac{1}{3} x - \frac{5}{6}$

Step 2

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

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

$m = - \frac{1}{3}$

$b = - \frac{5}{6}$

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

Slope: $- \frac{1}{3}$

y-intercept: $(0, - \frac{5}{6})$

Slope: $- \frac{1}{3}$

y-intercept: $(0, - \frac{5}{6})$

Step 3

Find the Slope and y-intercept -2x-6y=5

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