Pre-Algebra Examples

x - 3

$x - 3$ ,

y - \frac{1}{3}

$y - \frac{1}{3}$

Step 1

Graph

x - 3

$x - 3$ .

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Step 1.1

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

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Step 1.1.1

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 1.1.2

Find the values of

m

$m$ and

b

$b$ using the form

y = m x + b

$y = m x + b$ .

m = 1

$m = 1$

b = - 3

$b = - 3$

Step 1.1.3

The slope of the line is the value of

m

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

b

$b$ .

Slope:

1

$1$

y-intercept:

(0, - 3)

$(0, - 3)$

Slope:

1

$1$

y-intercept:

(0, - 3)

$(0, - 3)$

Step 1.2

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 1.2.1

Create a table of the

x

$x$ and

y

$y$ values.

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

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

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

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

Step 1.3

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

Slope:

1

$1$

y-intercept:

(0, - 3)

$(0, - 3)$

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

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

Slope:

1

$1$

y-intercept:

(0, - 3)

$(0, - 3)$

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

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

Step 2

Graph

y - \frac{1}{3}

$y - \frac{1}{3}$ .

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Step 2.1

Solve for

y

$y$ .

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Step 2.1.1

Rewrite the equation as

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

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

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

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

Step 2.1.2

Add

\frac{1}{3}

$\frac{1}{3}$ to both sides of the equation.

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

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

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

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

Step 2.2

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

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Step 2.2.1

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 2.2.2

Find the values of

m

$m$ and

b

$b$ using the form

y = m x + b

$y = m x + b$ .

m = 1

$m = 1$

b = \frac{1}{3}

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

Step 2.2.3

The slope of the line is the value of

m

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

b

$b$ .

Slope:

1

$1$

y-intercept:

(0, \frac{1}{3})

$(0, \frac{1}{3})$

Slope:

1

$1$

y-intercept:

(0, \frac{1}{3})

$(0, \frac{1}{3})$

Step 2.3

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 2.3.1

Find the x-intercept.

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Step 2.3.1.1

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

0

$0$ for

y

$y$ and solve for

x

$x$ .

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

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

Step 2.3.1.2

Solve the equation.

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Step 2.3.1.2.1

Rewrite the equation as

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

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

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

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

Step 2.3.1.2.2

Subtract

\frac{1}{3}

$\frac{1}{3}$ from both sides of the equation.

x = - \frac{1}{3}

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

x = - \frac{1}{3}

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

Step 2.3.1.3

x-intercept(s) in point form.

x-intercept(s):

(- \frac{1}{3}, 0)

$(- \frac{1}{3}, 0)$

x-intercept(s):

(- \frac{1}{3}, 0)

$(- \frac{1}{3}, 0)$

Step 2.3.2

Find the y-intercept.

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Step 2.3.2.1

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

0

$0$ for

x

$x$ and solve for

y

$y$ .

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

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

Step 2.3.2.2

Solve the equation.

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Step 2.3.2.2.1

Remove parentheses.

y = 0 + \frac{1}{3}

$y = 0 + \frac{1}{3}$

Step 2.3.2.2.2

Remove parentheses.

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

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

Step 2.3.2.2.3

Add

0

$0$ and

\frac{1}{3}

$\frac{1}{3}$ .

y = \frac{1}{3}

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

y = \frac{1}{3}

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

Step 2.3.2.3

y-intercept(s) in point form.

y-intercept(s):

(0, \frac{1}{3})

$(0, \frac{1}{3})$

y-intercept(s):

(0, \frac{1}{3})

$(0, \frac{1}{3})$

Step 2.3.3

Create a table of the

x

$x$ and

y

$y$ values.

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

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

Step 2.4

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

Slope:

$1$

y-intercept:

$(0, \frac{1}{3})$

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

Slope:

$1$

y-intercept:

$(0, \frac{1}{3})$

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

Step 3

Plot each graph on the same coordinate system.

$x - 3$

$y - \frac{1}{3}$

Step 4