Algebra Examples

x - 3 y = 6

$x - 3 y = 6$

Step 1

Solve for

y

$y$ .

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Step 1.1

Subtract

x

$x$ from both sides of the equation.

- 3 y = 6 - x

$- 3 y = 6 - x$

Step 1.2

Divide each term in

- 3 y = 6 - x

$- 3 y = 6 - x$ by

- 3

$- 3$ and simplify.

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Step 1.2.1

Divide each term in

- 3 y = 6 - x

$- 3 y = 6 - x$ by

- 3

$- 3$ .

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

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

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of

- 3

$- 3$ .

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Step 1.2.2.1.1

Cancel the common factor.

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

Step 1.2.2.1.2

Divide

$y$ by

$1$ .

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

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Divide

$6$ by

$- 3$ .

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

Step 1.2.3.1.2

Dividing two negative values results in a positive value.

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

Step 2

Rewrite in slope-intercept form.

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Step 2.1

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 2.2

Reorder

$- 2$ and

$\frac{x}{3}$ .

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

Step 2.3

Reorder terms.

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

Step 3

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

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Step 3.1

Find the values of

$m$ and

$b$ using the form

$y = m x + b$ .

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

$b = - 2$

Step 3.2

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:

$(0, - 2)$

Step 4

Any line can be graphed using two points. Select two

$x$ values, and plug them into the equation to find the corresponding

$y$ values.

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Step 4.1

Write in

$y = m x + b$ form.

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Step 4.1.1

Reorder

$- 2$ and

$\frac{x}{3}$ .

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

Step 4.1.2

Reorder terms.

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

Step 4.2

Create a table of the

$x$ and

$y$ values.

$\begin{array}{c} x & y \\ 0 & - 2 \\ 3 & - 1 \end{array}$

Step 5

Graph the line using the slope and the y-intercept, or the points.

Slope:

$\frac{1}{3}$

y-intercept:

$(0, - 2)$

$\begin{array}{c} x & y \\ 0 & - 2 \\ 3 & - 1 \end{array}$

Step 6