Algebra Examples

$x + 3 y = 6$

Rewrite in slope-intercept form.

Tap for more steps...

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 $x$ from both sides of the equation.

$3 y = 6 - x$

Divide each term in $3 y = 6 - x$ by $3$ and simplify.

Tap for more steps...

Divide each term in $3 y = 6 - x$ by $3$ .

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

Simplify the left side.

Tap for more steps...

Cancel the common factor of $3$ .

Tap for more steps...

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Tap for more steps...

Simplify each term.

Tap for more steps...

Divide $6$ by $3$ .

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

Move the negative in front of the fraction.

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

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

Tap for more steps...

Reorder $2$ and $- \frac{x}{3}$ .

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

Reorder terms.

$y = - (\frac{1}{3} x) + 2$

Remove parentheses.

$y = - \frac{1}{3} x + 2$

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

Tap for more steps...

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

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

$b = 2$

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: $(0, 2)$

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

y-intercept: $(0, 2)$