Algebra Examples

y = - \frac{1}{3} (x + 1) + 5

$y = - \frac{1}{3} (x + 1) + 5$

Step 1

Rewrite in slope-intercept form.

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Step 1.1

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 1.2

Write in

y = m x + b

$y = m x + b$ form.

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Step 1.2.1

Reorder terms.

y = - (\frac{1}{3} x) + \frac{14}{3}

$y = - (\frac{1}{3} x) + \frac{14}{3}$

Step 1.2.2

Remove parentheses.

y = - \frac{1}{3} x + \frac{14}{3}

$y = - \frac{1}{3} x + \frac{14}{3}$

y = - \frac{1}{3} x + \frac{14}{3}

$y = - \frac{1}{3} x + \frac{14}{3}$

y = - \frac{1}{3} x + \frac{14}{3}

$y = - \frac{1}{3} x + \frac{14}{3}$

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

$m$ and

b

$b$ using the form

y = m x + b

$y = m x + b$ .

m = - \frac{1}{3}

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

b = \frac{14}{3}

$b = \frac{14}{3}$

Step 2.2

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, \frac{14}{3})

$(0, \frac{14}{3})$

Slope:

- \frac{1}{3}

$- \frac{1}{3}$

y-intercept:

(0, \frac{14}{3})

$(0, \frac{14}{3})$

Step 3

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 3.1

Write in

y = m x + b

$y = m x + b$ form.

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Step 3.1.1

Reorder terms.

y = - (\frac{1}{3} x) + \frac{14}{3}

$y = - (\frac{1}{3} x) + \frac{14}{3}$

Step 3.1.2

Remove parentheses.

y = - \frac{1}{3} x + \frac{14}{3}

$y = - \frac{1}{3} x + \frac{14}{3}$

y = - \frac{1}{3} x + \frac{14}{3}

$y = - \frac{1}{3} x + \frac{14}{3}$

Step 3.2

Find the x-intercept.

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Step 3.2.1

To find the x-intercept(s), substitute in

0

$0$ for

y

$y$ and solve for

x

$x$ .

0 = - \frac{1}{3} x + \frac{14}{3}

$0 = - \frac{1}{3} x + \frac{14}{3}$

Step 3.2.2

Solve the equation.

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Step 3.2.2.1

Rewrite the equation as

- \frac{1}{3} x + \frac{14}{3} = 0

$- \frac{1}{3} x + \frac{14}{3} = 0$ .

- \frac{1}{3} x + \frac{14}{3} = 0

$- \frac{1}{3} x + \frac{14}{3} = 0$

Step 3.2.2.2

Combine

x

$x$ and

\frac{1}{3}

$\frac{1}{3}$ .

- \frac{x}{3} + \frac{14}{3} = 0

$- \frac{x}{3} + \frac{14}{3} = 0$

Step 3.2.2.3

Subtract

\frac{14}{3}

$\frac{14}{3}$ from both sides of the equation.

- \frac{x}{3} = - \frac{14}{3}

$- \frac{x}{3} = - \frac{14}{3}$

Step 3.2.2.4

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

- x = - 14

$- x = - 14$

Step 3.2.2.5

Divide each term in

- x = - 14

$- x = - 14$ by

- 1

$- 1$ and simplify.

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Step 3.2.2.5.1

Divide each term in

- x = - 14

$- x = - 14$ by

- 1

$- 1$ .

\frac{- x}{- 1} = \frac{- 14}{- 1}

$\frac{- x}{- 1} = \frac{- 14}{- 1}$

Step 3.2.2.5.2

Simplify the left side.

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Step 3.2.2.5.2.1

Dividing two negative values results in a positive value.

\frac{x}{1} = \frac{- 14}{- 1}

$\frac{x}{1} = \frac{- 14}{- 1}$

Step 3.2.2.5.2.2

Divide

x

$x$ by

1

$1$ .

x = \frac{- 14}{- 1}

$x = \frac{- 14}{- 1}$

x = \frac{- 14}{- 1}

$x = \frac{- 14}{- 1}$

Step 3.2.2.5.3

Simplify the right side.

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Step 3.2.2.5.3.1

Divide

- 14

$- 14$ by

- 1

$- 1$ .

x = 14

$x = 14$

x = 14

$x = 14$

x = 14

$x = 14$

x = 14

$x = 14$

Step 3.2.3

x-intercept(s) in point form.

x-intercept(s):

(14, 0)

$(14, 0)$

x-intercept(s):

(14, 0)

$(14, 0)$

Step 3.3

Find the y-intercept.

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Step 3.3.1

To find the y-intercept(s), substitute in

0

$0$ for

x

$x$ and solve for

y

$y$ .

y = - \frac{1}{3} \cdot 0 + \frac{14}{3}

$y = - \frac{1}{3} \cdot 0 + \frac{14}{3}$

Step 3.3.2

Solve the equation.

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Step 3.3.2.1

Remove parentheses.

y = - \frac{1}{3} \cdot 0 + \frac{14}{3}

$y = - \frac{1}{3} \cdot 0 + \frac{14}{3}$

Step 3.3.2.2

Simplify

- \frac{1}{3} \cdot 0 + \frac{14}{3}

$- \frac{1}{3} \cdot 0 + \frac{14}{3}$ .

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Step 3.3.2.2.1

Multiply

- \frac{1}{3} \cdot 0

$- \frac{1}{3} \cdot 0$ .

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Step 3.3.2.2.1.1

Multiply

0

$0$ by

- 1

$- 1$ .

y = 0 (\frac{1}{3}) + \frac{14}{3}

$y = 0 (\frac{1}{3}) + \frac{14}{3}$

Step 3.3.2.2.1.2

Multiply

0

$0$ by

\frac{1}{3}

$\frac{1}{3}$ .

y = 0 + \frac{14}{3}

$y = 0 + \frac{14}{3}$

y = 0 + \frac{14}{3}

$y = 0 + \frac{14}{3}$

Step 3.3.2.2.2

Add

0

$0$ and

\frac{14}{3}

$\frac{14}{3}$ .

y = \frac{14}{3}

$y = \frac{14}{3}$

y = \frac{14}{3}

$y = \frac{14}{3}$

y = \frac{14}{3}

$y = \frac{14}{3}$

Step 3.3.3

y-intercept(s) in point form.

y-intercept(s):

(0, \frac{14}{3})

$(0, \frac{14}{3})$

y-intercept(s):

(0, \frac{14}{3})

$(0, \frac{14}{3})$

Step 3.4

Create a table of the

x

$x$ and

y

$y$ values.

\begin{array}{c} x & y \\ 0 & \frac{14}{3} \\ 14 & 0 \end{array}

$\begin{array}{c} x & y \\ 0 & \frac{14}{3} \\ 14 & 0 \end{array}$

\begin{array}{c} x & y \\ 0 & \frac{14}{3} \\ 14 & 0 \end{array}

$\begin{array}{c} x & y \\ 0 & \frac{14}{3} \\ 14 & 0 \end{array}$

Step 4

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

Slope:

- \frac{1}{3}

$- \frac{1}{3}$

y-intercept:

(0, \frac{14}{3})

$(0, \frac{14}{3})$

\begin{array}{c} x & y \\ 0 & \frac{14}{3} \\ 14 & 0 \end{array}

$\begin{array}{c} x & y \\ 0 & \frac{14}{3} \\ 14 & 0 \end{array}$

Step 5