Pre-Algebra Examples

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

Step 1

Graph $x - 3$ .

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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 $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 1.1.2

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = 1$

$b = - 3$

Step 1.1.3

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $1$

y-intercept: $(0, - 3)$

Slope: $1$

y-intercept: $(0, - 3)$

Step 1.2

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 1.2.1

Create a table of the $x$ and $y$ values.

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

Step 1.3

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

Slope: $1$

y-intercept: $(0, - 3)$

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

Slope: $1$

y-intercept: $(0, - 3)$

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

Step 2

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

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Step 2.1

Solve for $y$ .

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Step 2.1.1

Rewrite the equation as $y - \frac{1}{3} = x$ .

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

Step 2.1.2

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

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

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 $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 2.2.2

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = 1$

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

Step 2.2.3

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $1$

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

Slope: $1$

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

Step 2.3

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 2.3.1

Find the x-intercept.

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Step 2.3.1.1

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

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

Step 2.3.1.2

Solve the equation.

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Step 2.3.1.2.1

Rewrite the equation as $x + \frac{1}{3} = 0$ .

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

Step 2.3.1.2.2

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

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

Step 2.3.1.3

x-intercept(s) in point form.

x-intercept(s): $(- \frac{1}{3}, 0)$

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 $0$ for $x$ and solve for $y$ .

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

Step 2.3.2.2

Solve the equation.

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Step 2.3.2.2.1

Remove parentheses.

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

Step 2.3.2.2.2

Remove parentheses.

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

Step 2.3.2.2.3

Add $0$ and $\frac{1}{3}$ .

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

Step 2.3.2.3

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{1}{3})$

Step 2.3.3

Create a table of the $x$ and $y$ values.

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

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