Pre-Algebra Examples

$- \frac{11}{13} x + \frac{10}{3}$

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

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

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Step 1.2.1

Reorder terms.

$y = - (\frac{11}{13} x) + \frac{10}{3}$

Step 1.2.2

Remove parentheses.

$y = - \frac{11}{13} x + \frac{10}{3}$

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 $y = m x + b$ .

$m = - \frac{11}{13}$

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

Step 2.2

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

Slope: $- \frac{11}{13}$

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

Slope: $- \frac{11}{13}$

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

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

Reorder terms.

$y = - (\frac{11}{13} x) + \frac{10}{3}$

Step 3.1.2

Remove parentheses.

$y = - \frac{11}{13} x + \frac{10}{3}$

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 $x$ .

$0 = - \frac{11}{13} x + \frac{10}{3}$

Step 3.2.2

Solve the equation.

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Step 3.2.2.1

Rewrite the equation as $- \frac{11}{13} x + \frac{10}{3} = 0$ .

$- \frac{11}{13} x + \frac{10}{3} = 0$

Step 3.2.2.2

Simplify each term.

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Step 3.2.2.2.1

Combine $x$ and $\frac{11}{13}$ .

$- \frac{x \cdot 11}{13} + \frac{10}{3} = 0$

Step 3.2.2.2.2

Move $11$ to the left of $x$ .

$- \frac{11 x}{13} + \frac{10}{3} = 0$

Step 3.2.2.3

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

$- \frac{11 x}{13} = - \frac{10}{3}$

Step 3.2.2.4

Multiply both sides of the equation by $- \frac{13}{11}$ .

$- \frac{13}{11} (- \frac{11 x}{13}) = - \frac{13}{11} (- \frac{10}{3})$

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

Simplify $- \frac{13}{11} (- \frac{11 x}{13})$ .

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Step 3.2.2.5.1.1.1

Cancel the common factor of $13$ .

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Step 3.2.2.5.1.1.1.1

Move the leading negative in $- \frac{13}{11}$ into the numerator.

$\frac{- 13}{11} (- \frac{11 x}{13}) = - \frac{13}{11} (- \frac{10}{3})$

Step 3.2.2.5.1.1.1.2

Move the leading negative in $- \frac{11 x}{13}$ into the numerator.

$\frac{- 13}{11} \cdot \frac{- 11 x}{13} = - \frac{13}{11} (- \frac{10}{3})$

Step 3.2.2.5.1.1.1.3

Factor $13$ out of $- 13$ .

$\frac{13 (- 1)}{11} \cdot \frac{- 11 x}{13} = - \frac{13}{11} (- \frac{10}{3})$

Step 3.2.2.5.1.1.1.4

Cancel the common factor.

$\frac{13 \cdot - 1}{11} \cdot \frac{- 11 x}{13} = - \frac{13}{11} (- \frac{10}{3})$

Step 3.2.2.5.1.1.1.5

Rewrite the expression.

$\frac{- 1}{11} (- 11 x) = - \frac{13}{11} (- \frac{10}{3})$

Step 3.2.2.5.1.1.2

Cancel the common factor of $11$ .

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Step 3.2.2.5.1.1.2.1

Factor $11$ out of $- 11 x$ .

$\frac{- 1}{11} (11 (- x)) = - \frac{13}{11} (- \frac{10}{3})$

Step 3.2.2.5.1.1.2.2

Cancel the common factor.

$\frac{- 1}{11} (11 (- x)) = - \frac{13}{11} (- \frac{10}{3})$

Step 3.2.2.5.1.1.2.3

Rewrite the expression.

$- - x = - \frac{13}{11} (- \frac{10}{3})$

Step 3.2.2.5.1.1.3

Multiply.

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Step 3.2.2.5.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{13}{11} (- \frac{10}{3})$

Step 3.2.2.5.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{13}{11} (- \frac{10}{3})$

Step 3.2.2.5.2

Simplify the right side.

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Step 3.2.2.5.2.1

Multiply $- \frac{13}{11} (- \frac{10}{3})$ .

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Step 3.2.2.5.2.1.1

Multiply $- 1$ by $- 1$ .

$x = 1 (\frac{13}{11}) \frac{10}{3}$

Step 3.2.2.5.2.1.2

Multiply $\frac{13}{11}$ by $1$ .

$x = \frac{13}{11} \cdot \frac{10}{3}$

Step 3.2.2.5.2.1.3

Multiply $\frac{13}{11}$ by $\frac{10}{3}$ .

$x = \frac{13 \cdot 10}{11 \cdot 3}$

Step 3.2.2.5.2.1.4

Multiply $13$ by $10$ .

$x = \frac{130}{11 \cdot 3}$

Step 3.2.2.5.2.1.5

Multiply $11$ by $3$ .

$x = \frac{130}{33}$

Step 3.2.3

x-intercept(s) in point form.

x-intercept(s): $(\frac{130}{33}, 0)$

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 $y$ .

$y = - \frac{11}{13} \cdot 0 + \frac{10}{3}$

Step 3.3.2

Solve the equation.

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Step 3.3.2.1

Remove parentheses.

$y = - \frac{11}{13} \cdot 0 + \frac{10}{3}$

Step 3.3.2.2

Simplify $- \frac{11}{13} \cdot 0 + \frac{10}{3}$ .

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Step 3.3.2.2.1

Multiply $- \frac{11}{13} \cdot 0$ .

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Step 3.3.2.2.1.1

Multiply $0$ by $- 1$ .

$y = 0 (\frac{11}{13}) + \frac{10}{3}$

Step 3.3.2.2.1.2

Multiply $0$ by $\frac{11}{13}$ .

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

Step 3.3.2.2.2

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

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

Step 3.3.3

y-intercept(s) in point form.

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

Step 3.4

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

$\begin{array}{c} x & y \\ 0 & \frac{10}{3} \\ \frac{130}{33} & 0 \end{array}$

Step 4

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

Slope: $- \frac{11}{13}$

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

$\begin{array}{c} x & y \\ 0 & \frac{10}{3} \\ \frac{130}{33} & 0 \end{array}$

Step 5