Find the Slope and y-intercept 6x-7y=21

$6 x - 7 y = 21$

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.

$y = m x + b$

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

$- 7 y = 21 - 6 x$

Divide each term in $- 7 y = 21 - 6 x$ by $- 7$ and simplify.

Divide each term in $- 7 y = 21 - 6 x$ by $- 7$ .

$\frac{- 7 y}{- 7} = \frac{21}{- 7} + \frac{- 6 x}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 y}{- 7} = \frac{21}{- 7} + \frac{- 6 x}{- 7}$

Divide $y$ by $1$ .

$y = \frac{21}{- 7} + \frac{- 6 x}{- 7}$

Simplify the right side.

Simplify each term.

Divide $21$ by $- 7$ .

$y = - 3 + \frac{- 6 x}{- 7}$

Dividing two negative values results in a positive value.

$y = - 3 + \frac{6 x}{7}$

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

Reorder $- 3$ and $\frac{6 x}{7}$ .

$y = \frac{6 x}{7} - 3$

Reorder terms.

$y = \frac{6}{7} x - 3$

Step 2

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

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

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

$b = - 3$

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: $(0, - 3)$

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

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

Step 3