Algebra Examples

$3 x + 2 y = 6$

Step 1

Rewrite in slope-intercept form.

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Step 1.1

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 1.2

Subtract

$3 x$ from both sides of the equation.

$2 y = 6 - 3 x$

Step 1.3

Divide each term in

$2 y = 6 - 3 x$ by

$2$ and simplify.

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Step 1.3.1

Divide each term in

$2 y = 6 - 3 x$ by

$2$ .

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

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of

$2$ .

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Step 1.3.2.1.1

Cancel the common factor.

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

Step 1.3.2.1.2

Divide

$y$ by

$1$ .

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

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

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

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Simplify each term.

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Step 1.3.3.1.1

Divide

$6$ by

$2$ .

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

Step 1.3.3.1.2

Move the negative in front of the fraction.

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

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

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

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

Step 1.4

Write in

$y = m x + b$ form.

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Step 1.4.1

Reorder

$3$ and

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

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

Step 1.4.2

Reorder terms.

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

Step 1.4.3

Remove parentheses.

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

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

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

Step 2

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

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Step 2.1

Find the values of

$m$ and

$b$ using the form

$y = m x + b$ .

$m = - \frac{3}{2}$

$b = 3$

Step 2.2

The slope of the line is the value of

$m$ , and the y-intercept is the value of

$b$ .

Slope:

$- \frac{3}{2}$

y-intercept:

$(0, 3)$

Slope:

$- \frac{3}{2}$

y-intercept:

$(0, 3)$

Step 3

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$