Finite Math Examples

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

Step 1

Substitute $- 2$ for $x$ and find the result for $y$ .

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

Step 2

Solve the equation for $y$ .

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Step 2.1

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

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

Step 2.2

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

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

Cancel the common factor of $2$ .

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Step 2.2.1.1.1

Factor $2$ out of $- 2$ .

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

Step 2.2.1.1.2

Cancel the common factor.

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

Step 2.2.1.1.3

Rewrite the expression.

$y = 3 \cdot - 1 - 1$

Step 2.2.1.2

Multiply $3$ by $- 1$ .

$y = - 3 - 1$

Step 2.2.2

Subtract $1$ from $- 3$ .

$y = - 4$

Step 3

Substitute $- 1$ for $x$ and find the result for $y$ .

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

Step 4

Solve the equation for $y$ .

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Step 4.1

Multiply $\frac{3}{2}$ by $- 1$ .

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

Step 4.2

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

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Step 4.2.1

Simplify each term.

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Step 4.2.1.1

Multiply $\frac{3}{2} \cdot - 1$ .

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Step 4.2.1.1.1

Combine $\frac{3}{2}$ and $- 1$ .

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

Step 4.2.1.1.2

Multiply $3$ by $- 1$ .

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

Step 4.2.1.2

Move the negative in front of the fraction.

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

Step 4.2.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 4.2.3

Combine $- 1$ and $\frac{2}{2}$ .

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

Step 4.2.4

Combine the numerators over the common denominator.

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

Step 4.2.5

Simplify the numerator.

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Step 4.2.5.1

Multiply $- 1$ by $2$ .

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

Step 4.2.5.2

Subtract $2$ from $- 3$ .

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

Step 4.2.6

Move the negative in front of the fraction.

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

Step 5

Substitute $0$ for $x$ and find the result for $y$ .

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

Step 6

Solve the equation for $y$ .

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Step 6.1

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

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

Step 6.2

Remove parentheses.

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

Step 6.3

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

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Step 6.3.1

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

$y = 0 - 1$

Step 6.3.2

Subtract $1$ from $0$ .

$y = - 1$

Step 7

Substitute $1$ for $x$ and find the result for $y$ .

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

Step 8

Solve the equation for $y$ .

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Step 8.1

Multiply $\frac{3}{2}$ by $1$ .

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

Step 8.2

Remove parentheses.

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

Step 8.3

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

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Step 8.3.1

Multiply $\frac{3}{2}$ by $1$ .

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

Step 8.3.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 8.3.3

Combine $- 1$ and $\frac{2}{2}$ .

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

Step 8.3.4

Combine the numerators over the common denominator.

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

Step 8.3.5

Simplify the numerator.

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Step 8.3.5.1

Multiply $- 1$ by $2$ .

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

Step 8.3.5.2

Subtract $2$ from $3$ .

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

Step 9

Substitute $2$ for $x$ and find the result for $y$ .

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

Step 10

Solve the equation for $y$ .

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Step 10.1

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

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

Step 10.2

Remove parentheses.

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

Step 10.3

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

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Step 10.3.1

Cancel the common factor of $2$ .

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Step 10.3.1.1

Cancel the common factor.

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

Step 10.3.1.2

Rewrite the expression.

$y = 3 - 1$

Step 10.3.2

Subtract $1$ from $3$ .

$y = 2$

Step 11

This is a table of possible values to use when graphing the equation.

$\begin{array}{c} x & y \\ - 2 & - 4 \\ - 1 & - \frac{5}{2} \\ 0 & - 1 \\ 1 & \frac{1}{2} \\ 2 & 2 \end{array}$

Step 12