Finite Math Examples

$y = 3 x + \frac{17}{2}$

Step 1

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

$y = 3 (- 2) + \frac{17}{2}$

Step 2

Simplify $3 (- 2) + \frac{17}{2}$ .

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Step 2.1

Multiply $3$ by $- 2$ .

$y = - 6 + \frac{17}{2}$

Step 2.2

To write $- 6$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = - 6 \cdot \frac{2}{2} + \frac{17}{2}$

Step 2.3

Combine $- 6$ and $\frac{2}{2}$ .

$y = \frac{- 6 \cdot 2}{2} + \frac{17}{2}$

Step 2.4

Combine the numerators over the common denominator.

$y = \frac{- 6 \cdot 2 + 17}{2}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $- 6$ by $2$ .

$y = \frac{- 12 + 17}{2}$

Step 2.5.2

Add $- 12$ and $17$ .

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

Step 3

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

$y = 3 (- 1) + \frac{17}{2}$

Step 4

Simplify $3 (- 1) + \frac{17}{2}$ .

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Step 4.1

Multiply $3$ by $- 1$ .

$y = - 3 + \frac{17}{2}$

Step 4.2

To write $- 3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = - 3 \cdot \frac{2}{2} + \frac{17}{2}$

Step 4.3

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

$y = \frac{- 3 \cdot 2}{2} + \frac{17}{2}$

Step 4.4

Combine the numerators over the common denominator.

$y = \frac{- 3 \cdot 2 + 17}{2}$

Step 4.5

Simplify the numerator.

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Step 4.5.1

Multiply $- 3$ by $2$ .

$y = \frac{- 6 + 17}{2}$

Step 4.5.2

Add $- 6$ and $17$ .

$y = \frac{11}{2}$

Step 5

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

$y = 3 (0) + \frac{17}{2}$

Step 6

Solve the equation for $y$ .

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Step 6.1

Remove parentheses.

$y = 3 (0) + \frac{17}{2}$

Step 6.2

Simplify $3 (0) + \frac{17}{2}$ .

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Step 6.2.1

Multiply $3$ by $0$ .

$y = 0 + \frac{17}{2}$

Step 6.2.2

Add $0$ and $\frac{17}{2}$ .

$y = \frac{17}{2}$

Step 7

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

$y = 3 (1) + \frac{17}{2}$

Step 8

Solve the equation for $y$ .

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Step 8.1

Remove parentheses.

$y = 3 (1) + \frac{17}{2}$

Step 8.2

Simplify $3 (1) + \frac{17}{2}$ .

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Step 8.2.1

Multiply $3$ by $1$ .

$y = 3 + \frac{17}{2}$

Step 8.2.2

To write $3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = 3 \cdot \frac{2}{2} + \frac{17}{2}$

Step 8.2.3

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

$y = \frac{3 \cdot 2}{2} + \frac{17}{2}$

Step 8.2.4

Combine the numerators over the common denominator.

$y = \frac{3 \cdot 2 + 17}{2}$

Step 8.2.5

Simplify the numerator.

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Step 8.2.5.1

Multiply $3$ by $2$ .

$y = \frac{6 + 17}{2}$

Step 8.2.5.2

Add $6$ and $17$ .

$y = \frac{23}{2}$

Step 9

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

$y = 3 (2) + \frac{17}{2}$

Step 10

Solve the equation for $y$ .

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Step 10.1

Remove parentheses.

$y = 3 (2) + \frac{17}{2}$

Step 10.2

Simplify $3 (2) + \frac{17}{2}$ .

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Step 10.2.1

Multiply $3$ by $2$ .

$y = 6 + \frac{17}{2}$

Step 10.2.2

To write $6$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = 6 \cdot \frac{2}{2} + \frac{17}{2}$

Step 10.2.3

Combine $6$ and $\frac{2}{2}$ .

$y = \frac{6 \cdot 2}{2} + \frac{17}{2}$

Step 10.2.4

Combine the numerators over the common denominator.

$y = \frac{6 \cdot 2 + 17}{2}$

Step 10.2.5

Simplify the numerator.

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Step 10.2.5.1

Multiply $6$ by $2$ .

$y = \frac{12 + 17}{2}$

Step 10.2.5.2

Add $12$ and $17$ .

$y = \frac{29}{2}$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & \frac{5}{2} \\ - 1 & \frac{11}{2} \\ 0 & \frac{17}{2} \\ 1 & \frac{23}{2} \\ 2 & \frac{29}{2} \end{array}$

Step 12