Pre-Algebra Examples

$f (x) = \frac{10 - 2 x}{3}$

Step 1

Rewrite the function as an equation.

$y = \frac{2 (5 - x)}{3}$

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

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

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Step 2.2.1

Apply the distributive property.

$y = \frac{2 \cdot 5 + 2 (- x)}{3}$

Step 2.2.2

Multiply $2$ by $5$ .

$y = \frac{10 + 2 (- x)}{3}$

Step 2.2.3

Multiply $- 1$ by $2$ .

$y = \frac{10 - 2 x}{3}$

Step 2.2.4

Split the fraction $\frac{10 - 2 x}{3}$ into two fractions.

$y = \frac{10}{3} + \frac{- 2 x}{3}$

Step 2.2.5

Move the negative in front of the fraction.

$y = \frac{10}{3} - \frac{2 x}{3}$

Step 2.2.6

Rearrange terms.

$y = - \frac{2 x}{3} + \frac{10}{3}$

Step 2.2.7

Reorder terms.

$y = - (\frac{2}{3} x) + \frac{10}{3}$

Step 2.2.8

Remove parentheses.

$y = - \frac{2}{3} x + \frac{10}{3}$

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 $y = m x + b$ .

$m = - \frac{2}{3}$

$b = \frac{10}{3}$

Step 3.2

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

Slope: $- \frac{2}{3}$

y-intercept: $(0, \frac{10}{3})$

Slope: $- \frac{2}{3}$

y-intercept: $(0, \frac{10}{3})$

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

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

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Step 4.1.1

Apply the distributive property.

$y = \frac{2 \cdot 5 + 2 (- x)}{3}$

Step 4.1.2

Multiply $2$ by $5$ .

$y = \frac{10 + 2 (- x)}{3}$

Step 4.1.3

Multiply $- 1$ by $2$ .

$y = \frac{10 - 2 x}{3}$

Step 4.1.4

Split the fraction $\frac{10 - 2 x}{3}$ into two fractions.

$y = \frac{10}{3} + \frac{- 2 x}{3}$

Step 4.1.5

Move the negative in front of the fraction.

$y = \frac{10}{3} - \frac{2 x}{3}$

Step 4.1.6

Rearrange terms.

$y = - \frac{2 x}{3} + \frac{10}{3}$

Step 4.1.7

Reorder terms.

$y = - (\frac{2}{3} x) + \frac{10}{3}$

Step 4.1.8

Remove parentheses.

$y = - \frac{2}{3} x + \frac{10}{3}$

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 $x$ .

$0 = - \frac{2}{3} x + \frac{10}{3}$

Step 4.2.2

Solve the equation.

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Step 4.2.2.1

Rewrite the equation as $- \frac{2}{3} x + \frac{10}{3} = 0$ .

$- \frac{2}{3} x + \frac{10}{3} = 0$

Step 4.2.2.2

Simplify each term.

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Step 4.2.2.2.1

Combine $x$ and $\frac{2}{3}$ .

$- \frac{x \cdot 2}{3} + \frac{10}{3} = 0$

Step 4.2.2.2.2

Move $2$ to the left of $x$ .

$- \frac{2 x}{3} + \frac{10}{3} = 0$

Step 4.2.2.3

Subtract $\frac{10}{3}$ from both sides of the equation.

$- \frac{2 x}{3} = - \frac{10}{3}$

Step 4.2.2.4

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

$- 2 x = - 10$

Step 4.2.2.5

Divide each term in $- 2 x = - 10$ by $- 2$ and simplify.

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Step 4.2.2.5.1

Divide each term in $- 2 x = - 10$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 10}{- 2}$

Step 4.2.2.5.2

Simplify the left side.

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Step 4.2.2.5.2.1

Cancel the common factor of $- 2$ .

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Step 4.2.2.5.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 10}{- 2}$

Step 4.2.2.5.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 10}{- 2}$

Step 4.2.2.5.3

Simplify the right side.

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Step 4.2.2.5.3.1

Divide $- 10$ by $- 2$ .

$x = 5$

Step 4.2.3

x-intercept(s) in point form.

x-intercept(s): $(5, 0)$

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 $y$ .

$y = - \frac{2}{3} \cdot 0 + \frac{10}{3}$

Step 4.3.2

Solve the equation.

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Step 4.3.2.1

Remove parentheses.

$y = - \frac{2}{3} \cdot 0 + \frac{10}{3}$

Step 4.3.2.2

Simplify $- \frac{2}{3} \cdot 0 + \frac{10}{3}$ .

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Step 4.3.2.2.1

Multiply $- \frac{2}{3} \cdot 0$ .

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Step 4.3.2.2.1.1

Multiply $0$ by $- 1$ .

$y = 0 (\frac{2}{3}) + \frac{10}{3}$

Step 4.3.2.2.1.2

Multiply $0$ by $\frac{2}{3}$ .

$y = 0 + \frac{10}{3}$

Step 4.3.2.2.2

Add $0$ and $\frac{10}{3}$ .

$y = \frac{10}{3}$

Step 4.3.3

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{10}{3})$

Step 4.4

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

$\begin{array}{c} x & y \\ 0 & \frac{10}{3} \\ 5 & 0 \end{array}$

Step 5

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

Slope: $- \frac{2}{3}$

y-intercept: $(0, \frac{10}{3})$

$\begin{array}{c} x & y \\ 0 & \frac{10}{3} \\ 5 & 0 \end{array}$

Step 6