Algebra Examples

$3 Y - 2 = 3 (X - 3)$

Step 1

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

$3 Y - 2 = 3 (X - 3)$

Step 2

Solve the equation for $y$ .

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Step 2.1

Simplify $3 (X - 3)$ .

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Step 2.1.1

Rewrite.

$3 Y - 2 = 0 + 0 + 3 (X - 3)$

Step 2.1.2

Simplify by adding zeros.

$3 Y - 2 = 3 (X - 3)$

Step 2.1.3

Apply the distributive property.

$3 Y - 2 = 3 X + 3 \cdot - 3$

Step 2.1.4

Multiply $3$ by $- 3$ .

$3 Y - 2 = 3 X - 9$

Step 2.2

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

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Step 2.2.1

Add $2$ to both sides of the equation.

$3 Y = 3 X - 9 + 2$

Step 2.2.2

Add $- 9$ and $2$ .

$3 Y = 3 X - 7$

Step 2.3

Divide each term in $3 Y = 3 X - 7$ by $3$ and simplify.

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Step 2.3.1

Divide each term in $3 Y = 3 X - 7$ by $3$ .

$\frac{3 Y}{3} = \frac{3 X}{3} + \frac{- 7}{3}$

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.

$\frac{3 Y}{3} = \frac{3 X}{3} + \frac{- 7}{3}$

Step 2.3.2.1.2

Divide $Y$ by $1$ .

$Y = \frac{3 X}{3} + \frac{- 7}{3}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Simplify each term.

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Step 2.3.3.1.1

Cancel the common factor of $3$ .

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Step 2.3.3.1.1.1

Cancel the common factor.

$Y = \frac{3 X}{3} + \frac{- 7}{3}$

Step 2.3.3.1.1.2

Divide $X$ by $1$ .

$Y = X + \frac{- 7}{3}$

Step 2.3.3.1.2

Move the negative in front of the fraction.

$Y = X - \frac{7}{3}$

Step 3

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

$3 Y - 2 = 3 (X - 3)$

Step 4

Solve the equation for $y$ .

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Step 4.1

Simplify $3 (X - 3)$ .

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Step 4.1.1

Rewrite.

$3 Y - 2 = 0 + 0 + 3 (X - 3)$

Step 4.1.2

Simplify by adding zeros.

$3 Y - 2 = 3 (X - 3)$

Step 4.1.3

Apply the distributive property.

$3 Y - 2 = 3 X + 3 \cdot - 3$

Step 4.1.4

Multiply $3$ by $- 3$ .

$3 Y - 2 = 3 X - 9$

Step 4.2

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

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Step 4.2.1

Add $2$ to both sides of the equation.

$3 Y = 3 X - 9 + 2$

Step 4.2.2

Add $- 9$ and $2$ .

$3 Y = 3 X - 7$

Step 4.3

Divide each term in $3 Y = 3 X - 7$ by $3$ and simplify.

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Step 4.3.1

Divide each term in $3 Y = 3 X - 7$ by $3$ .

$\frac{3 Y}{3} = \frac{3 X}{3} + \frac{- 7}{3}$

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.

$\frac{3 Y}{3} = \frac{3 X}{3} + \frac{- 7}{3}$

Step 4.3.2.1.2

Divide $Y$ by $1$ .

$Y = \frac{3 X}{3} + \frac{- 7}{3}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Simplify each term.

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Step 4.3.3.1.1

Cancel the common factor of $3$ .

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Step 4.3.3.1.1.1

Cancel the common factor.

$Y = \frac{3 X}{3} + \frac{- 7}{3}$

Step 4.3.3.1.1.2

Divide $X$ by $1$ .

$Y = X + \frac{- 7}{3}$

Step 4.3.3.1.2

Move the negative in front of the fraction.

$Y = X - \frac{7}{3}$

Step 5

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

$3 Y - 2 = 3 (X - 3)$

Step 6

Solve the equation for $y$ .

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Step 6.1

Simplify $3 (X - 3)$ .

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Step 6.1.1

Rewrite.

$3 Y - 2 = 0 + 0 + 3 (X - 3)$

Step 6.1.2

Simplify by adding zeros.

$3 Y - 2 = 3 (X - 3)$

Step 6.1.3

Apply the distributive property.

$3 Y - 2 = 3 X + 3 \cdot - 3$

Step 6.1.4

Multiply $3$ by $- 3$ .

$3 Y - 2 = 3 X - 9$

Step 6.2

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

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Step 6.2.1

Add $2$ to both sides of the equation.

$3 Y = 3 X - 9 + 2$

Step 6.2.2

Add $- 9$ and $2$ .

$3 Y = 3 X - 7$

Step 6.3

Divide each term in $3 Y = 3 X - 7$ by $3$ and simplify.

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Step 6.3.1

Divide each term in $3 Y = 3 X - 7$ by $3$ .

$\frac{3 Y}{3} = \frac{3 X}{3} + \frac{- 7}{3}$

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.

$\frac{3 Y}{3} = \frac{3 X}{3} + \frac{- 7}{3}$

Step 6.3.2.1.2

Divide $Y$ by $1$ .

$Y = \frac{3 X}{3} + \frac{- 7}{3}$

Step 6.3.3

Simplify the right side.

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Step 6.3.3.1

Simplify each term.

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Step 6.3.3.1.1

Cancel the common factor of $3$ .

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Step 6.3.3.1.1.1

Cancel the common factor.

$Y = \frac{3 X}{3} + \frac{- 7}{3}$

Step 6.3.3.1.1.2

Divide $X$ by $1$ .

$Y = X + \frac{- 7}{3}$

Step 6.3.3.1.2

Move the negative in front of the fraction.

$Y = X - \frac{7}{3}$

Step 7

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

$3 Y - 2 = 3 (X - 3)$

Step 8

Solve the equation for $y$ .

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Step 8.1

Simplify $3 (X - 3)$ .

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Step 8.1.1

Rewrite.

$3 Y - 2 = 0 + 0 + 3 (X - 3)$

Step 8.1.2

Simplify by adding zeros.

$3 Y - 2 = 3 (X - 3)$

Step 8.1.3

Apply the distributive property.

$3 Y - 2 = 3 X + 3 \cdot - 3$

Step 8.1.4

Multiply $3$ by $- 3$ .

$3 Y - 2 = 3 X - 9$

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 $2$ to both sides of the equation.

$3 Y = 3 X - 9 + 2$

Step 8.2.2

Add $- 9$ and $2$ .

$3 Y = 3 X - 7$

Step 8.3

Divide each term in $3 Y = 3 X - 7$ by $3$ and simplify.

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Step 8.3.1

Divide each term in $3 Y = 3 X - 7$ by $3$ .

$\frac{3 Y}{3} = \frac{3 X}{3} + \frac{- 7}{3}$

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.

$\frac{3 Y}{3} = \frac{3 X}{3} + \frac{- 7}{3}$

Step 8.3.2.1.2

Divide $Y$ by $1$ .

$Y = \frac{3 X}{3} + \frac{- 7}{3}$

Step 8.3.3

Simplify the right side.

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Step 8.3.3.1

Simplify each term.

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Step 8.3.3.1.1

Cancel the common factor of $3$ .

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Step 8.3.3.1.1.1

Cancel the common factor.

$Y = \frac{3 X}{3} + \frac{- 7}{3}$

Step 8.3.3.1.1.2

Divide $X$ by $1$ .

$Y = X + \frac{- 7}{3}$

Step 8.3.3.1.2

Move the negative in front of the fraction.

$Y = X - \frac{7}{3}$

Step 9

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

$3 Y - 2 = 3 (X - 3)$

Step 10

Solve the equation for $y$ .

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Step 10.1

Simplify $3 (X - 3)$ .

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Step 10.1.1

Rewrite.

$3 Y - 2 = 0 + 0 + 3 (X - 3)$

Step 10.1.2

Simplify by adding zeros.

$3 Y - 2 = 3 (X - 3)$

Step 10.1.3

Apply the distributive property.

$3 Y - 2 = 3 X + 3 \cdot - 3$

Step 10.1.4

Multiply $3$ by $- 3$ .

$3 Y - 2 = 3 X - 9$

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 $2$ to both sides of the equation.

$3 Y = 3 X - 9 + 2$

Step 10.2.2

Add $- 9$ and $2$ .

$3 Y = 3 X - 7$

Step 10.3

Divide each term in $3 Y = 3 X - 7$ by $3$ and simplify.

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Step 10.3.1

Divide each term in $3 Y = 3 X - 7$ by $3$ .

$\frac{3 Y}{3} = \frac{3 X}{3} + \frac{- 7}{3}$

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.

$\frac{3 Y}{3} = \frac{3 X}{3} + \frac{- 7}{3}$

Step 10.3.2.1.2

Divide $Y$ by $1$ .

$Y = \frac{3 X}{3} + \frac{- 7}{3}$

Step 10.3.3

Simplify the right side.

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Step 10.3.3.1

Simplify each term.

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Step 10.3.3.1.1

Cancel the common factor of $3$ .

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Step 10.3.3.1.1.1

Cancel the common factor.

$Y = \frac{3 X}{3} + \frac{- 7}{3}$

Step 10.3.3.1.1.2

Divide $X$ by $1$ .

$Y = X + \frac{- 7}{3}$

Step 10.3.3.1.2

Move the negative in front of the fraction.

$Y = X - \frac{7}{3}$

Step 11

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

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

Step 12