Finite Math Examples

$5 x - 3 y + 15 = 0$

Step 1

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

$5 (- 2) - 3 y + 15 = 0$

Step 2

Solve the equation for $y$ .

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Step 2.1

Simplify $5 (- 2) - 3 y + 15$ .

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Step 2.1.1

Multiply $5$ by $- 2$ .

$- 10 - 3 y + 15 = 0$

Step 2.1.2

Add $- 10$ and $15$ .

$- 3 y + 5 = 0$

Step 2.2

Subtract $5$ from both sides of the equation.

$- 3 y = - 5$

Step 2.3

Divide each term in $- 3 y = - 5$ by $- 3$ and simplify.

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Step 2.3.1

Divide each term in $- 3 y = - 5$ by $- 3$ .

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

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $- 3$ .

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Step 2.3.2.1.1

Cancel the common factor.

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

Step 2.3.2.1.2

Divide $y$ by $1$ .

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

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Dividing two negative values results in a positive value.

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

Step 3

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

$5 (- 1) - 3 y + 15 = 0$

Step 4

Solve the equation for $y$ .

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Step 4.1

Simplify $5 (- 1) - 3 y + 15$ .

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Step 4.1.1

Multiply $5$ by $- 1$ .

$- 5 - 3 y + 15 = 0$

Step 4.1.2

Add $- 5$ and $15$ .

$- 3 y + 10 = 0$

Step 4.2

Subtract $10$ from both sides of the equation.

$- 3 y = - 10$

Step 4.3

Divide each term in $- 3 y = - 10$ by $- 3$ and simplify.

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Step 4.3.1

Divide each term in $- 3 y = - 10$ by $- 3$ .

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

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $- 3$ .

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Step 4.3.2.1.1

Cancel the common factor.

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

Step 4.3.2.1.2

Divide $y$ by $1$ .

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

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Dividing two negative values results in a positive value.

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

Step 5

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

$5 (0) - 3 y + 15 = 0$

Step 6

Solve the equation for $y$ .

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Step 6.1

Simplify $5 (0) - 3 y + 15$ .

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Step 6.1.1

Multiply $5$ by $0$ .

$0 - 3 y + 15 = 0$

Step 6.1.2

Subtract $3 y$ from $0$ .

$- 3 y + 15 = 0$

Step 6.2

Subtract $15$ from both sides of the equation.

$- 3 y = - 15$

Step 6.3

Divide each term in $- 3 y = - 15$ by $- 3$ and simplify.

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Step 6.3.1

Divide each term in $- 3 y = - 15$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{- 15}{- 3}$

Step 6.3.2

Simplify the left side.

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Step 6.3.2.1

Cancel the common factor of $- 3$ .

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Step 6.3.2.1.1

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{- 15}{- 3}$

Step 6.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 15}{- 3}$

Step 6.3.3

Simplify the right side.

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Step 6.3.3.1

Divide $- 15$ by $- 3$ .

$y = 5$

Step 7

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

$5 (1) - 3 y + 15 = 0$

Step 8

Solve the equation for $y$ .

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Step 8.1

Simplify $5 (1) - 3 y + 15$ .

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Step 8.1.1

Multiply $5$ by $1$ .

$5 - 3 y + 15 = 0$

Step 8.1.2

Add $5$ and $15$ .

$- 3 y + 20 = 0$

Step 8.2

Subtract $20$ from both sides of the equation.

$- 3 y = - 20$

Step 8.3

Divide each term in $- 3 y = - 20$ by $- 3$ and simplify.

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Step 8.3.1

Divide each term in $- 3 y = - 20$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{- 20}{- 3}$

Step 8.3.2

Simplify the left side.

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Step 8.3.2.1

Cancel the common factor of $- 3$ .

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Step 8.3.2.1.1

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{- 20}{- 3}$

Step 8.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 20}{- 3}$

Step 8.3.3

Simplify the right side.

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Step 8.3.3.1

Dividing two negative values results in a positive value.

$y = \frac{20}{3}$

Step 9

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

$5 (2) - 3 y + 15 = 0$

Step 10

Solve the equation for $y$ .

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Step 10.1

Simplify $5 (2) - 3 y + 15$ .

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Step 10.1.1

Multiply $5$ by $2$ .

$10 - 3 y + 15 = 0$

Step 10.1.2

Add $10$ and $15$ .

$- 3 y + 25 = 0$

Step 10.2

Subtract $25$ from both sides of the equation.

$- 3 y = - 25$

Step 10.3

Divide each term in $- 3 y = - 25$ by $- 3$ and simplify.

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Step 10.3.1

Divide each term in $- 3 y = - 25$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{- 25}{- 3}$

Step 10.3.2

Simplify the left side.

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Step 10.3.2.1

Cancel the common factor of $- 3$ .

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Step 10.3.2.1.1

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{- 25}{- 3}$

Step 10.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 25}{- 3}$

Step 10.3.3

Simplify the right side.

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Step 10.3.3.1

Dividing two negative values results in a positive value.

$y = \frac{25}{3}$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & \frac{5}{3} \\ - 1 & \frac{10}{3} \\ 0 & 5 \\ 1 & \frac{20}{3} \\ 2 & \frac{25}{3} \end{array}$

Step 12