Calculus Examples

$2 x + 3 y - 6 = 0$

Step 1

The slope-intercept form is

$y = m x + b$ , where

$m$ is the slope and

$b$ is the y-intercept.

$y = m x + b$

Step 2

Rewrite in slope-intercept form.

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Step 2.1

Move all terms not containing

$y$ to the right side of the equation.

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Step 2.1.1

Subtract

$2 x$ from both sides of the equation.

$3 y - 6 = - 2 x$

Step 2.1.2

Add

$6$ to both sides of the equation.

$3 y = - 2 x + 6$

$3 y = - 2 x + 6$

Step 2.2

Divide each term in

$3 y = - 2 x + 6$ by

$3$ and simplify.

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Step 2.2.1

Divide each term in

$3 y = - 2 x + 6$ by

$3$ .

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

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of

$3$ .

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Step 2.2.2.1.1

Cancel the common factor.

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

Step 2.2.2.1.2

Divide

$y$ by

$1$ .

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

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

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

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Simplify each term.

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Step 2.2.3.1.1

Move the negative in front of the fraction.

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

Step 2.2.3.1.2

Divide

$6$ by

$3$ .

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

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

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

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

Step 2.3

Write in

$y = m x + b$ form.

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Step 2.3.1

Reorder terms.

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

Step 2.3.2

Remove parentheses.

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

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

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

$2 x + 3 y - 6 = 0$

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