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}

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

Step 1.2.2.1.2

Divide

y

$y$ by

1

$1$ .

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

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

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

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

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

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

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

$6$ by

3

$3$ .

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

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

Step 1.2.3.1.2

Move the negative in front of the fraction.

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

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

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

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

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

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

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

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

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

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

Step 2

Rewrite in slope-intercept form.

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Step 2.1

The slope-intercept form is

y = m x + b

$y = m x + b$ , where

m

$m$ is the slope and

b

$b$ is the y-intercept.

y = m x + b

$y = m x + b$

Step 2.2

Reorder

2

$2$ and

- \frac{x}{3}

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

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

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

Step 2.3

Write in

y = m x + b

$y = m x + b$ form.

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Step 2.3.1

Reorder terms.

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

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

Step 2.3.2

Remove parentheses.

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

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

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

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

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

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

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

$m$ and

b

$b$ using the form

y = m x + b

$y = m x + b$ .

m = - \frac{1}{3}

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

b = 2

$b = 2$

Step 3.2

The slope of the line is the value of

m

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

b

$b$ .

Slope:

- \frac{1}{3}

$- \frac{1}{3}$

y-intercept:

(0, 2)

$(0, 2)$

Slope:

- \frac{1}{3}

$- \frac{1}{3}$

y-intercept:

(0, 2)

$(0, 2)$

Step 4

Any line can be graphed using two points. Select two

x

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

y

$y$ values.

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Step 4.1

Write in

y = m x + b

$y = m x + b$ form.

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Step 4.1.1

Reorder

2

$2$ and

- \frac{x}{3}

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

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

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

Step 4.1.2

Reorder terms.

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

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

Step 4.1.3

Remove parentheses.

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

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

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

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

Step 4.2

Create a table of the

x

$x$ and

y

$y$ values.

\begin{matrix} x & y 0 & 2 3 & 1 \end{matrix}

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

\begin{matrix} x & y 0 & 2 3 & 1 \end{matrix}

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

Step 5

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

Slope:

- \frac{1}{3}

$- \frac{1}{3}$

y-intercept:

(0, 2)

$(0, 2)$

\begin{matrix} x & y 0 & 2 3 & 1 \end{matrix}

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

Step 6