Find the Slope and y-intercept -x+6y-42=0

$- x + 6 y - 42 = 0$

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 $x$ to both sides of the equation.

$6 y - 42 = x$

Add $42$ to both sides of the equation.

$6 y = x + 42$

Divide each term in $6 y = x + 42$ by $6$ and simplify.

Divide each term in $6 y = x + 42$ by $6$ .

$\frac{6 y}{6} = \frac{x}{6} + \frac{42}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 y}{6} = \frac{x}{6} + \frac{42}{6}$

Divide $y$ by $1$ .

$y = \frac{x}{6} + \frac{42}{6}$

Simplify the right side.

Divide $42$ by $6$ .

$y = \frac{x}{6} + 7$

Reorder terms.

$y = \frac{1}{6} x + 7$

Step 2

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

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

$m = \frac{1}{6}$

$b = 7$

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

Slope: $\frac{1}{6}$

y-intercept: $(0, 7)$

Slope: $\frac{1}{6}$

y-intercept: $(0, 7)$

Step 3