Pre-Algebra Examples

$f (x) = \frac{5}{4} x - \frac{5}{2}$

Step 1

Rewrite the function as an equation.

$y = \frac{5 x}{4} - \frac{5}{2}$

Step 2

Rewrite in slope-intercept form.

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Step 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

Reorder terms.

$y = \frac{5}{4} x - \frac{5}{2}$

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

$m = \frac{5}{4}$

$b = - \frac{5}{2}$

Step 3.2

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

Slope: $\frac{5}{4}$

y-intercept: $(0, - \frac{5}{2})$

Slope: $\frac{5}{4}$

y-intercept: $(0, - \frac{5}{2})$

Step 4

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 4.1

Reorder terms.

$y = \frac{5}{4} x - \frac{5}{2}$

Step 4.2

Find the x-intercept.

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Step 4.2.1

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

$0 = \frac{5}{4} x - \frac{5}{2}$

Step 4.2.2

Solve the equation.

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Step 4.2.2.1

Rewrite the equation as $\frac{5}{4} x - \frac{5}{2} = 0$ .

$\frac{5}{4} x - \frac{5}{2} = 0$

Step 4.2.2.2

Combine $\frac{5}{4}$ and $x$ .

$\frac{5 x}{4} - \frac{5}{2} = 0$

Step 4.2.2.3

Add $\frac{5}{2}$ to both sides of the equation.

$\frac{5 x}{4} = \frac{5}{2}$

Step 4.2.2.4

Multiply both sides of the equation by $\frac{4}{5}$ .

$\frac{4}{5} \cdot \frac{5 x}{4} = \frac{4}{5} \cdot \frac{5}{2}$

Step 4.2.2.5

Simplify both sides of the equation.

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Step 4.2.2.5.1

Simplify the left side.

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Step 4.2.2.5.1.1

Simplify $\frac{4}{5} \cdot \frac{5 x}{4}$ .

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Step 4.2.2.5.1.1.1

Cancel the common factor of $4$ .

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Step 4.2.2.5.1.1.1.1

Cancel the common factor.

$\frac{4}{5} \cdot \frac{5 x}{4} = \frac{4}{5} \cdot \frac{5}{2}$

Step 4.2.2.5.1.1.1.2

Rewrite the expression.

$\frac{1}{5} (5 x) = \frac{4}{5} \cdot \frac{5}{2}$

Step 4.2.2.5.1.1.2

Cancel the common factor of $5$ .

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Step 4.2.2.5.1.1.2.1

Factor $5$ out of $5 x$ .

$\frac{1}{5} (5 (x)) = \frac{4}{5} \cdot \frac{5}{2}$

Step 4.2.2.5.1.1.2.2

Cancel the common factor.

$\frac{1}{5} (5 x) = \frac{4}{5} \cdot \frac{5}{2}$

Step 4.2.2.5.1.1.2.3

Rewrite the expression.

$x = \frac{4}{5} \cdot \frac{5}{2}$

Step 4.2.2.5.2

Simplify the right side.

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Step 4.2.2.5.2.1

Simplify $\frac{4}{5} \cdot \frac{5}{2}$ .

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Step 4.2.2.5.2.1.1

Cancel the common factor of $2$ .

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Step 4.2.2.5.2.1.1.1

Factor $2$ out of $4$ .

$x = \frac{2 (2)}{5} \cdot \frac{5}{2}$

Step 4.2.2.5.2.1.1.2

Cancel the common factor.

$x = \frac{2 \cdot 2}{5} \cdot \frac{5}{2}$

Step 4.2.2.5.2.1.1.3

Rewrite the expression.

$x = \frac{2}{5} \cdot 5$

Step 4.2.2.5.2.1.2

Cancel the common factor of $5$ .

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Step 4.2.2.5.2.1.2.1

Cancel the common factor.

$x = \frac{2}{5} \cdot 5$

Step 4.2.2.5.2.1.2.2

Rewrite the expression.

$x = 2$

Step 4.2.3

x-intercept(s) in point form.

x-intercept(s): $(2, 0)$

Step 4.3

Find the y-intercept.

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Step 4.3.1

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

$y = \frac{5}{4} \cdot (0) - \frac{5}{2}$

Step 4.3.2

Solve the equation.

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Step 4.3.2.1

Multiply $\frac{5}{4}$ by $0$ .

$y = \frac{5}{4} \cdot 0 - \frac{5}{2}$

Step 4.3.2.2

Remove parentheses.

$y = \frac{5}{4} \cdot (0) - \frac{5}{2}$

Step 4.3.2.3

Simplify $\frac{5}{4} \cdot (0) - \frac{5}{2}$ .

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Step 4.3.2.3.1

Multiply $\frac{5}{4}$ by $0$ .

$y = 0 - \frac{5}{2}$

Step 4.3.2.3.2

Subtract $\frac{5}{2}$ from $0$ .

$y = - \frac{5}{2}$

Step 4.3.3

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{5}{2})$

Step 4.4

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

$\begin{array}{c} x & y \\ 0 & - \frac{5}{2} \\ 2 & 0 \end{array}$

Step 5

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

Slope: $\frac{5}{4}$

y-intercept: $(0, - \frac{5}{2})$

$\begin{array}{c} x & y \\ 0 & - \frac{5}{2} \\ 2 & 0 \end{array}$

Step 6