Finite Math Examples

$9 y - 4 x = 12$

Step 1

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

$9 y - 4 \cdot - 2 = 12$

Step 2

Solve the equation for $y$ .

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Step 2.1

Multiply $- 4$ by $- 2$ .

$9 y + 8 = 12$

Step 2.2

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

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Step 2.2.1

Subtract $8$ from both sides of the equation.

$9 y = 12 - 8$

Step 2.2.2

Subtract $8$ from $12$ .

$9 y = 4$

Step 2.3

Divide each term in $9 y = 4$ by $9$ and simplify.

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Step 2.3.1

Divide each term in $9 y = 4$ by $9$ .

$\frac{9 y}{9} = \frac{4}{9}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $9$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{9 y}{9} = \frac{4}{9}$

Step 2.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{4}{9}$

Step 3

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

$9 y - 4 \cdot - 1 = 12$

Step 4

Solve the equation for $y$ .

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Step 4.1

Multiply $- 4$ by $- 1$ .

$9 y + 4 = 12$

Step 4.2

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

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Step 4.2.1

Subtract $4$ from both sides of the equation.

$9 y = 12 - 4$

Step 4.2.2

Subtract $4$ from $12$ .

$9 y = 8$

Step 4.3

Divide each term in $9 y = 8$ by $9$ and simplify.

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Step 4.3.1

Divide each term in $9 y = 8$ by $9$ .

$\frac{9 y}{9} = \frac{8}{9}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $9$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{9 y}{9} = \frac{8}{9}$

Step 4.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{8}{9}$

Step 5

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

$9 y - 4 \cdot 0 = 12$

Step 6

Solve the equation for $y$ .

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Step 6.1

Simplify $9 y - 4 \cdot 0$ .

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Step 6.1.1

Multiply $- 4$ by $0$ .

$9 y + 0 = 12$

Step 6.1.2

Add $9 y$ and $0$ .

$9 y = 12$

Step 6.2

Divide each term in $9 y = 12$ by $9$ and simplify.

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Step 6.2.1

Divide each term in $9 y = 12$ by $9$ .

$\frac{9 y}{9} = \frac{12}{9}$

Step 6.2.2

Simplify the left side.

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Step 6.2.2.1

Cancel the common factor of $9$ .

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Step 6.2.2.1.1

Cancel the common factor.

$\frac{9 y}{9} = \frac{12}{9}$

Step 6.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{12}{9}$

Step 6.2.3

Simplify the right side.

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Step 6.2.3.1

Cancel the common factor of $12$ and $9$ .

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Step 6.2.3.1.1

Factor $3$ out of $12$ .

$y = \frac{3 (4)}{9}$

Step 6.2.3.1.2

Cancel the common factors.

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Step 6.2.3.1.2.1

Factor $3$ out of $9$ .

$y = \frac{3 \cdot 4}{3 \cdot 3}$

Step 6.2.3.1.2.2

Cancel the common factor.

$y = \frac{3 \cdot 4}{3 \cdot 3}$

Step 6.2.3.1.2.3

Rewrite the expression.

$y = \frac{4}{3}$

Step 7

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

$9 y - 4 \cdot 1 = 12$

Step 8

Solve the equation for $y$ .

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Step 8.1

Multiply $- 4$ by $1$ .

$9 y - 4 = 12$

Step 8.2

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

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Step 8.2.1

Add $4$ to both sides of the equation.

$9 y = 12 + 4$

Step 8.2.2

Add $12$ and $4$ .

$9 y = 16$

Step 8.3

Divide each term in $9 y = 16$ by $9$ and simplify.

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Step 8.3.1

Divide each term in $9 y = 16$ by $9$ .

$\frac{9 y}{9} = \frac{16}{9}$

Step 8.3.2

Simplify the left side.

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Step 8.3.2.1

Cancel the common factor of $9$ .

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Step 8.3.2.1.1

Cancel the common factor.

$\frac{9 y}{9} = \frac{16}{9}$

Step 8.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{16}{9}$

Step 9

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

$9 y - 4 \cdot 2 = 12$

Step 10

Solve the equation for $y$ .

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Step 10.1

Multiply $- 4$ by $2$ .

$9 y - 8 = 12$

Step 10.2

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

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Step 10.2.1

Add $8$ to both sides of the equation.

$9 y = 12 + 8$

Step 10.2.2

Add $12$ and $8$ .

$9 y = 20$

Step 10.3

Divide each term in $9 y = 20$ by $9$ and simplify.

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Step 10.3.1

Divide each term in $9 y = 20$ by $9$ .

$\frac{9 y}{9} = \frac{20}{9}$

Step 10.3.2

Simplify the left side.

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Step 10.3.2.1

Cancel the common factor of $9$ .

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Step 10.3.2.1.1

Cancel the common factor.

$\frac{9 y}{9} = \frac{20}{9}$

Step 10.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{20}{9}$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & \frac{4}{9} \\ - 1 & \frac{8}{9} \\ 0 & \frac{4}{3} \\ 1 & \frac{16}{9} \\ 2 & \frac{20}{9} \end{array}$

Step 12