Precalculus Examples

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

Step 1

Rewrite in slope-intercept form.

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Step 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 1.2

Simplify $\frac{x - 3}{6}$ .

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Step 1.2.1

Split the fraction $\frac{x - 3}{6}$ into two fractions.

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

Step 1.2.2

Simplify each term.

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Step 1.2.2.1

Cancel the common factor of $- 3$ and $6$ .

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Step 1.2.2.1.1

Factor $3$ out of $- 3$ .

$y = \frac{x}{6} + \frac{3 (- 1)}{6}$

Step 1.2.2.1.2

Cancel the common factors.

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Step 1.2.2.1.2.1

Factor $3$ out of $6$ .

$y = \frac{x}{6} + \frac{3 \cdot - 1}{3 \cdot 2}$

Step 1.2.2.1.2.2

Cancel the common factor.

$y = \frac{x}{6} + \frac{3 \cdot - 1}{3 \cdot 2}$

Step 1.2.2.1.2.3

Rewrite the expression.

$y = \frac{x}{6} + \frac{- 1}{2}$

Step 1.2.2.2

Move the negative in front of the fraction.

$y = \frac{x}{6} - \frac{1}{2}$

Step 1.3

Reorder terms.

$y = \frac{1}{6} x - \frac{1}{2}$

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

$m = \frac{1}{6}$

$b = - \frac{1}{2}$

Step 2.2

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

Slope: $\frac{1}{6}$

y-intercept: $(0, - \frac{1}{2})$

Slope: $\frac{1}{6}$

y-intercept: $(0, - \frac{1}{2})$

Step 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 3.1

Write in $y = m x + b$ form.

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Step 3.1.1

Split the fraction $\frac{x - 3}{6}$ into two fractions.

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

Step 3.1.2

Cancel the common factor of $- 3$ and $6$ .

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Step 3.1.2.1

Factor $3$ out of $- 3$ .

$y = \frac{x}{6} + \frac{3 (- 1)}{6}$

Step 3.1.2.2

Cancel the common factors.

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Step 3.1.2.2.1

Factor $3$ out of $6$ .

$y = \frac{x}{6} + \frac{3 \cdot - 1}{3 \cdot 2}$

Step 3.1.2.2.2

Cancel the common factor.

$y = \frac{x}{6} + \frac{3 \cdot - 1}{3 \cdot 2}$

Step 3.1.2.2.3

Rewrite the expression.

$y = \frac{x}{6} + \frac{- 1}{2}$

Step 3.1.3

Move the negative in front of the fraction.

$y = \frac{x}{6} - \frac{1}{2}$

Step 3.1.4

Reorder terms.

$y = \frac{1}{6} x - \frac{1}{2}$

Step 3.2

Find the x-intercept.

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Step 3.2.1

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

$0 = \frac{1}{6} x - \frac{1}{2}$

Step 3.2.2

Solve the equation.

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Step 3.2.2.1

Rewrite the equation as $\frac{1}{6} x - \frac{1}{2} = 0$ .

$\frac{1}{6} x - \frac{1}{2} = 0$

Step 3.2.2.2

Combine $\frac{1}{6}$ and $x$ .

$\frac{x}{6} - \frac{1}{2} = 0$

Step 3.2.2.3

Add $\frac{1}{2}$ to both sides of the equation.

$\frac{x}{6} = \frac{1}{2}$

Step 3.2.2.4

Multiply both sides of the equation by $6$ .

$6 \frac{x}{6} = 6 (\frac{1}{2})$

Step 3.2.2.5

Simplify both sides of the equation.

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Step 3.2.2.5.1

Simplify the left side.

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Step 3.2.2.5.1.1

Cancel the common factor of $6$ .

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Step 3.2.2.5.1.1.1

Cancel the common factor.

$6 \frac{x}{6} = 6 (\frac{1}{2})$

Step 3.2.2.5.1.1.2

Rewrite the expression.

$x = 6 (\frac{1}{2})$

Step 3.2.2.5.2

Simplify the right side.

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Step 3.2.2.5.2.1

Cancel the common factor of $2$ .

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Step 3.2.2.5.2.1.1

Factor $2$ out of $6$ .

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

Step 3.2.2.5.2.1.2

Cancel the common factor.

$x = 2 \cdot 3 \frac{1}{2}$

Step 3.2.2.5.2.1.3

Rewrite the expression.

$x = 3$

Step 3.2.3

x-intercept(s) in point form.

x-intercept(s): $(3, 0)$

Step 3.3

Find the y-intercept.

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Step 3.3.1

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

$y = \frac{1}{6} \cdot (0) - \frac{1}{2}$

Step 3.3.2

Solve the equation.

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Step 3.3.2.1

Multiply $\frac{1}{6}$ by $0$ .

$y = \frac{1}{6} \cdot 0 - \frac{1}{2}$

Step 3.3.2.2

Remove parentheses.

$y = \frac{1}{6} \cdot (0) - \frac{1}{2}$

Step 3.3.2.3

Simplify $\frac{1}{6} \cdot (0) - \frac{1}{2}$ .

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Step 3.3.2.3.1

Multiply $\frac{1}{6}$ by $0$ .

$y = 0 - \frac{1}{2}$

Step 3.3.2.3.2

Subtract $\frac{1}{2}$ from $0$ .

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

Step 3.3.3

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{1}{2})$

Step 3.4

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

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

Step 4

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

Slope: $\frac{1}{6}$

y-intercept: $(0, - \frac{1}{2})$

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

Step 5