Finite Math Examples

$8 x = - 4 y + 12$

Step 1

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

$8 (- 2) = - 4 y + 12$

Step 2

Solve the equation for $y$ .

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Step 2.1

Rewrite the equation as $- 4 y + 12 = 8 (- 2)$ .

$- 4 y + 12 = 8 (- 2)$

Step 2.2

Multiply $8$ by $- 2$ .

$- 4 y + 12 = - 16$

Step 2.3

Move all terms not containing $y$ to the right side of the equation.

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Step 2.3.1

Subtract $12$ from both sides of the equation.

$- 4 y = - 16 - 12$

Step 2.3.2

Subtract $12$ from $- 16$ .

$- 4 y = - 28$

Step 2.4

Divide each term in $- 4 y = - 28$ by $- 4$ and simplify.

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Step 2.4.1

Divide each term in $- 4 y = - 28$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{- 28}{- 4}$

Step 2.4.2

Simplify the left side.

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Step 2.4.2.1

Cancel the common factor of $- 4$ .

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Step 2.4.2.1.1

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{- 28}{- 4}$

Step 2.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 28}{- 4}$

Step 2.4.3

Simplify the right side.

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Step 2.4.3.1

Divide $- 28$ by $- 4$ .

$y = 7$

Step 3

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

$8 (- 1) = - 4 y + 12$

Step 4

Solve the equation for $y$ .

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Step 4.1

Rewrite the equation as $- 4 y + 12 = 8 (- 1)$ .

$- 4 y + 12 = 8 (- 1)$

Step 4.2

Multiply $8$ by $- 1$ .

$- 4 y + 12 = - 8$

Step 4.3

Move all terms not containing $y$ to the right side of the equation.

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Step 4.3.1

Subtract $12$ from both sides of the equation.

$- 4 y = - 8 - 12$

Step 4.3.2

Subtract $12$ from $- 8$ .

$- 4 y = - 20$

Step 4.4

Divide each term in $- 4 y = - 20$ by $- 4$ and simplify.

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Step 4.4.1

Divide each term in $- 4 y = - 20$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{- 20}{- 4}$

Step 4.4.2

Simplify the left side.

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Step 4.4.2.1

Cancel the common factor of $- 4$ .

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Step 4.4.2.1.1

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{- 20}{- 4}$

Step 4.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 20}{- 4}$

Step 4.4.3

Simplify the right side.

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Step 4.4.3.1

Divide $- 20$ by $- 4$ .

$y = 5$

Step 5

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

$8 (0) = - 4 y + 12$

Step 6

Solve the equation for $y$ .

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Step 6.1

Rewrite the equation as $- 4 y + 12 = 8 (0)$ .

$- 4 y + 12 = 8 (0)$

Step 6.2

Multiply $8$ by $0$ .

$- 4 y + 12 = 0$

Step 6.3

Subtract $12$ from both sides of the equation.

$- 4 y = - 12$

Step 6.4

Divide each term in $- 4 y = - 12$ by $- 4$ and simplify.

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Step 6.4.1

Divide each term in $- 4 y = - 12$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{- 12}{- 4}$

Step 6.4.2

Simplify the left side.

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Step 6.4.2.1

Cancel the common factor of $- 4$ .

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Step 6.4.2.1.1

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{- 12}{- 4}$

Step 6.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 12}{- 4}$

Step 6.4.3

Simplify the right side.

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Step 6.4.3.1

Divide $- 12$ by $- 4$ .

$y = 3$

Step 7

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

$8 (1) = - 4 y + 12$

Step 8

Solve the equation for $y$ .

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Step 8.1

Rewrite the equation as $- 4 y + 12 = 8 (1)$ .

$- 4 y + 12 = 8 (1)$

Step 8.2

Multiply $8$ by $1$ .

$- 4 y + 12 = 8$

Step 8.3

Move all terms not containing $y$ to the right side of the equation.

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Step 8.3.1

Subtract $12$ from both sides of the equation.

$- 4 y = 8 - 12$

Step 8.3.2

Subtract $12$ from $8$ .

$- 4 y = - 4$

Step 8.4

Divide each term in $- 4 y = - 4$ by $- 4$ and simplify.

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Step 8.4.1

Divide each term in $- 4 y = - 4$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{- 4}{- 4}$

Step 8.4.2

Simplify the left side.

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Step 8.4.2.1

Cancel the common factor of $- 4$ .

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Step 8.4.2.1.1

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{- 4}{- 4}$

Step 8.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 4}{- 4}$

Step 8.4.3

Simplify the right side.

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Step 8.4.3.1

Divide $- 4$ by $- 4$ .

$y = 1$

Step 9

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

$8 (2) = - 4 y + 12$

Step 10

Solve the equation for $y$ .

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Step 10.1

Rewrite the equation as $- 4 y + 12 = 8 (2)$ .

$- 4 y + 12 = 8 (2)$

Step 10.2

Multiply $8$ by $2$ .

$- 4 y + 12 = 16$

Step 10.3

Move all terms not containing $y$ to the right side of the equation.

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Step 10.3.1

Subtract $12$ from both sides of the equation.

$- 4 y = 16 - 12$

Step 10.3.2

Subtract $12$ from $16$ .

$- 4 y = 4$

Step 10.4

Divide each term in $- 4 y = 4$ by $- 4$ and simplify.

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Step 10.4.1

Divide each term in $- 4 y = 4$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{4}{- 4}$

Step 10.4.2

Simplify the left side.

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Step 10.4.2.1

Cancel the common factor of $- 4$ .

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Step 10.4.2.1.1

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{4}{- 4}$

Step 10.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{4}{- 4}$

Step 10.4.3

Simplify the right side.

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Step 10.4.3.1

Divide $4$ by $- 4$ .

$y = - 1$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & 7 \\ - 1 & 5 \\ 0 & 3 \\ 1 & 1 \\ 2 & - 1 \end{array}$

Step 12