Finite Math Examples

$y = \frac{3}{5} x + 1$

Step 1

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

$y = \frac{3}{5} \cdot (- 2) + 1$

Step 2

Solve the equation for $y$ .

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Step 2.1

Multiply $\frac{3}{5}$ by $- 2$ .

$y = \frac{3}{5} \cdot - 2 + 1$

Step 2.2

Simplify $\frac{3}{5} \cdot - 2 + 1$ .

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Step 2.2.1

Simplify each term.

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Step 2.2.1.1

Multiply $\frac{3}{5} \cdot - 2$ .

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Step 2.2.1.1.1

Combine $\frac{3}{5}$ and $- 2$ .

$y = \frac{3 \cdot - 2}{5} + 1$

Step 2.2.1.1.2

Multiply $3$ by $- 2$ .

$y = \frac{- 6}{5} + 1$

Step 2.2.1.2

Move the negative in front of the fraction.

$y = - \frac{6}{5} + 1$

Step 2.2.2

Simplify the expression.

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Step 2.2.2.1

Write $1$ as a fraction with a common denominator.

$y = - \frac{6}{5} + \frac{5}{5}$

Step 2.2.2.2

Combine the numerators over the common denominator.

$y = \frac{- 6 + 5}{5}$

Step 2.2.2.3

Add $- 6$ and $5$ .

$y = \frac{- 1}{5}$

Step 2.2.2.4

Move the negative in front of the fraction.

$y = - \frac{1}{5}$

Step 3

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

$y = \frac{3}{5} \cdot (- 1) + 1$

Step 4

Solve the equation for $y$ .

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Step 4.1

Multiply $\frac{3}{5}$ by $- 1$ .

$y = \frac{3}{5} \cdot - 1 + 1$

Step 4.2

Simplify $\frac{3}{5} \cdot - 1 + 1$ .

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Step 4.2.1

Simplify each term.

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Step 4.2.1.1

Multiply $\frac{3}{5} \cdot - 1$ .

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Step 4.2.1.1.1

Combine $\frac{3}{5}$ and $- 1$ .

$y = \frac{3 \cdot - 1}{5} + 1$

Step 4.2.1.1.2

Multiply $3$ by $- 1$ .

$y = \frac{- 3}{5} + 1$

Step 4.2.1.2

Move the negative in front of the fraction.

$y = - \frac{3}{5} + 1$

Step 4.2.2

Simplify the expression.

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Step 4.2.2.1

Write $1$ as a fraction with a common denominator.

$y = - \frac{3}{5} + \frac{5}{5}$

Step 4.2.2.2

Combine the numerators over the common denominator.

$y = \frac{- 3 + 5}{5}$

Step 4.2.2.3

Add $- 3$ and $5$ .

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

Step 5

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

$y = \frac{3}{5} \cdot (0) + 1$

Step 6

Solve the equation for $y$ .

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Step 6.1

Multiply $\frac{3}{5}$ by $0$ .

$y = \frac{3}{5} \cdot 0 + 1$

Step 6.2

Remove parentheses.

$y = \frac{3}{5} \cdot (0) + 1$

Step 6.3

Simplify $\frac{3}{5} \cdot (0) + 1$ .

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Step 6.3.1

Multiply $\frac{3}{5}$ by $0$ .

$y = 0 + 1$

Step 6.3.2

Add $0$ and $1$ .

$y = 1$

Step 7

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

$y = \frac{3}{5} \cdot (1) + 1$

Step 8

Solve the equation for $y$ .

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Step 8.1

Multiply $\frac{3}{5}$ by $1$ .

$y = \frac{3}{5} \cdot 1 + 1$

Step 8.2

Remove parentheses.

$y = \frac{3}{5} \cdot (1) + 1$

Step 8.3

Simplify $\frac{3}{5} \cdot (1) + 1$ .

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Step 8.3.1

Multiply $\frac{3}{5}$ by $1$ .

$y = \frac{3}{5} + 1$

Step 8.3.2

Simplify the expression.

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Step 8.3.2.1

Write $1$ as a fraction with a common denominator.

$y = \frac{3}{5} + \frac{5}{5}$

Step 8.3.2.2

Combine the numerators over the common denominator.

$y = \frac{3 + 5}{5}$

Step 8.3.2.3

Add $3$ and $5$ .

$y = \frac{8}{5}$

Step 9

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

$y = \frac{3}{5} \cdot (2) + 1$

Step 10

Solve the equation for $y$ .

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Step 10.1

Multiply $\frac{3}{5}$ by $2$ .

$y = \frac{3}{5} \cdot 2 + 1$

Step 10.2

Remove parentheses.

$y = \frac{3}{5} \cdot (2) + 1$

Step 10.3

Simplify $\frac{3}{5} \cdot (2) + 1$ .

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Step 10.3.1

Multiply $\frac{3}{5} (2)$ .

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Step 10.3.1.1

Combine $\frac{3}{5}$ and $2$ .

$y = \frac{3 \cdot 2}{5} + 1$

Step 10.3.1.2

Multiply $3$ by $2$ .

$y = \frac{6}{5} + 1$

Step 10.3.2

Simplify the expression.

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Step 10.3.2.1

Write $1$ as a fraction with a common denominator.

$y = \frac{6}{5} + \frac{5}{5}$

Step 10.3.2.2

Combine the numerators over the common denominator.

$y = \frac{6 + 5}{5}$

Step 10.3.2.3

Add $6$ and $5$ .

$y = \frac{11}{5}$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & - \frac{1}{5} \\ - 1 & \frac{2}{5} \\ 0 & 1 \\ 1 & \frac{8}{5} \\ 2 & \frac{11}{5} \end{array}$

Step 12