Find the Slope and y-intercept 6x+7y-42=0

$6 x + 7 y - 42 = 0$

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.

Subtract $6 x$ from both sides of the equation.

$7 y - 42 = - 6 x$

Add $42$ to both sides of the equation.

$7 y = - 6 x + 42$

Divide each term in $7 y = - 6 x + 42$ by $7$ and simplify.

Divide each term in $7 y = - 6 x + 42$ by $7$ .

$\frac{7 y}{7} = \frac{- 6 x}{7} + \frac{42}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 y}{7} = \frac{- 6 x}{7} + \frac{42}{7}$

Divide $y$ by $1$ .

$y = \frac{- 6 x}{7} + \frac{42}{7}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{(6) x}{7} + \frac{42}{7}$

Divide $42$ by $7$ .

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

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

Reorder terms.

$y = - (\frac{6}{7} x) + 6$

Remove parentheses.

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

Step 2

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

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

$m = - \frac{6}{7}$

$b = 6$

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

Slope: $- \frac{6}{7}$

y-intercept: $(0, 6)$

Slope: $- \frac{6}{7}$

y-intercept: $(0, 6)$

Step 3