Algebra Examples

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

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.

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

Step 1.2.2

Remove parentheses.

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

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 $y = m x + b$ .

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

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

Step 2.2

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

Slope: $- \frac{1}{3}$

y-intercept: $(0, - \frac{3}{2})$

Slope: $- \frac{1}{3}$

y-intercept: $(0, - \frac{3}{2})$

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

Reorder terms.

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

Step 3.1.2

Remove parentheses.

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

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 $x$ .

$0 = - \frac{1}{3} x - \frac{3}{2}$

Step 3.2.2

Solve the equation.

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Step 3.2.2.1

Rewrite the equation as $- \frac{1}{3} x - \frac{3}{2} = 0$ .

$- \frac{1}{3} x - \frac{3}{2} = 0$

Step 3.2.2.2

Combine $x$ and $\frac{1}{3}$ .

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

Step 3.2.2.3

Add $\frac{3}{2}$ to both sides of the equation.

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

Step 3.2.2.4

Multiply both sides of the equation by $- 3$ .

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

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

Simplify $- 3 (- \frac{x}{3})$ .

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Step 3.2.2.5.1.1.1

Cancel the common factor of $3$ .

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Step 3.2.2.5.1.1.1.1

Move the leading negative in $- \frac{x}{3}$ into the numerator.

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

Step 3.2.2.5.1.1.1.2

Factor $3$ out of $- 3$ .

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

Step 3.2.2.5.1.1.1.3

Cancel the common factor.

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

Step 3.2.2.5.1.1.1.4

Rewrite the expression.

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

Step 3.2.2.5.1.1.2

Multiply.

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Step 3.2.2.5.1.1.2.1

Multiply $- 1$ by $- 1$ .

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

Step 3.2.2.5.1.1.2.2

Multiply $x$ by $1$ .

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

Step 3.2.2.5.2

Simplify the right side.

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Step 3.2.2.5.2.1

Simplify $- 3 (\frac{3}{2})$ .

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Step 3.2.2.5.2.1.1

Multiply $- 3 (\frac{3}{2})$ .

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Step 3.2.2.5.2.1.1.1

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

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

Step 3.2.2.5.2.1.1.2

Multiply $- 3$ by $3$ .

$x = \frac{- 9}{2}$

Step 3.2.2.5.2.1.2

Move the negative in front of the fraction.

$x = - \frac{9}{2}$

Step 3.2.3

x-intercept(s) in point form.

x-intercept(s): $(- \frac{9}{2}, 0)$

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 $y$ .

$y = - \frac{1}{3} \cdot 0 - \frac{3}{2}$

Step 3.3.2

Solve the equation.

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Step 3.3.2.1

Remove parentheses.

$y = - \frac{1}{3} \cdot 0 - \frac{3}{2}$

Step 3.3.2.2

Simplify $- \frac{1}{3} \cdot 0 - \frac{3}{2}$ .

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Step 3.3.2.2.1

Multiply $- \frac{1}{3} \cdot 0$ .

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Step 3.3.2.2.1.1

Multiply $0$ by $- 1$ .

$y = 0 (\frac{1}{3}) - \frac{3}{2}$

Step 3.3.2.2.1.2

Multiply $0$ by $\frac{1}{3}$ .

$y = 0 - \frac{3}{2}$

Step 3.3.2.2.2

Subtract $\frac{3}{2}$ from $0$ .

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

Step 3.3.3

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{3}{2})$

Step 3.4

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

$\begin{array}{c} x & y \\ - \frac{9}{2} & 0 \\ 0 & - \frac{3}{2} \end{array}$

Step 4

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

Slope: $- \frac{1}{3}$

y-intercept: $(0, - \frac{3}{2})$

$\begin{array}{c} x & y \\ - \frac{9}{2} & 0 \\ 0 & - \frac{3}{2} \end{array}$

Step 5