Algebra Examples

$2 Y - 2 = \frac{3}{4} (X - 4)$

Step 1

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

$2 Y - 2 = \frac{3}{4} \cdot (X - 4)$

Step 2

Solve the equation for $y$ .

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Step 2.1

Simplify $\frac{3}{4} \cdot (X - 4)$ .

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Step 2.1.1

Rewrite.

$2 Y - 2 = 0 + 0 + \frac{3}{4} \cdot (X - 4)$

Step 2.1.2

Simplify by adding zeros.

$2 Y - 2 = \frac{3}{4} \cdot (X - 4)$

Step 2.1.3

Apply the distributive property.

$2 Y - 2 = \frac{3}{4} X + \frac{3}{4} \cdot - 4$

Step 2.1.4

Combine $\frac{3}{4}$ and $X$ .

$2 Y - 2 = \frac{3 X}{4} + \frac{3}{4} \cdot - 4$

Step 2.1.5

Cancel the common factor of $4$ .

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Step 2.1.5.1

Factor $4$ out of $- 4$ .

$2 Y - 2 = \frac{3 X}{4} + \frac{3}{4} \cdot (4 (- 1))$

Step 2.1.5.2

Cancel the common factor.

$2 Y - 2 = \frac{3 X}{4} + \frac{3}{4} \cdot (4 \cdot - 1)$

Step 2.1.5.3

Rewrite the expression.

$2 Y - 2 = \frac{3 X}{4} + 3 \cdot - 1$

Step 2.1.6

Multiply $3$ by $- 1$ .

$2 Y - 2 = \frac{3 X}{4} - 3$

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.

$2 Y = \frac{3 X}{4} - 3 + 2$

Step 2.2.2

Add $- 3$ and $2$ .

$2 Y = \frac{3 X}{4} - 1$

Step 2.3

Divide each term in $2 Y = \frac{3 X}{4} - 1$ by $2$ and simplify.

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Step 2.3.1

Divide each term in $2 Y = \frac{3 X}{4} - 1$ by $2$ .

$\frac{2 Y}{2} = \frac{\frac{3 X}{4}}{2} + \frac{- 1}{2}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $2$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{2 Y}{2} = \frac{\frac{3 X}{4}}{2} + \frac{- 1}{2}$

Step 2.3.2.1.2

Divide $Y$ by $1$ .

$Y = \frac{\frac{3 X}{4}}{2} + \frac{- 1}{2}$

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

Multiply the numerator by the reciprocal of the denominator.

$Y = \frac{3 X}{4} \cdot \frac{1}{2} + \frac{- 1}{2}$

Step 2.3.3.1.2

Multiply $\frac{3 X}{4} \cdot \frac{1}{2}$ .

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Step 2.3.3.1.2.1

Multiply $\frac{3 X}{4}$ by $\frac{1}{2}$ .

$Y = \frac{3 X}{4 \cdot 2} + \frac{- 1}{2}$

Step 2.3.3.1.2.2

Multiply $4$ by $2$ .

$Y = \frac{3 X}{8} + \frac{- 1}{2}$

Step 2.3.3.1.3

Move the negative in front of the fraction.

$Y = \frac{3 X}{8} - \frac{1}{2}$

Step 3

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

$2 Y - 2 = \frac{3}{4} \cdot (X - 4)$

Step 4

Solve the equation for $y$ .

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Step 4.1

Simplify $\frac{3}{4} \cdot (X - 4)$ .

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Step 4.1.1

Rewrite.

$2 Y - 2 = 0 + 0 + \frac{3}{4} \cdot (X - 4)$

Step 4.1.2

Simplify by adding zeros.

$2 Y - 2 = \frac{3}{4} \cdot (X - 4)$

Step 4.1.3

Apply the distributive property.

$2 Y - 2 = \frac{3}{4} X + \frac{3}{4} \cdot - 4$

Step 4.1.4

Combine $\frac{3}{4}$ and $X$ .

$2 Y - 2 = \frac{3 X}{4} + \frac{3}{4} \cdot - 4$

Step 4.1.5

Cancel the common factor of $4$ .

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Step 4.1.5.1

Factor $4$ out of $- 4$ .

$2 Y - 2 = \frac{3 X}{4} + \frac{3}{4} \cdot (4 (- 1))$

Step 4.1.5.2

Cancel the common factor.

$2 Y - 2 = \frac{3 X}{4} + \frac{3}{4} \cdot (4 \cdot - 1)$

Step 4.1.5.3

Rewrite the expression.

$2 Y - 2 = \frac{3 X}{4} + 3 \cdot - 1$

Step 4.1.6

Multiply $3$ by $- 1$ .

$2 Y - 2 = \frac{3 X}{4} - 3$

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.

$2 Y = \frac{3 X}{4} - 3 + 2$

Step 4.2.2

Add $- 3$ and $2$ .

$2 Y = \frac{3 X}{4} - 1$

Step 4.3

Divide each term in $2 Y = \frac{3 X}{4} - 1$ by $2$ and simplify.

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Step 4.3.1

Divide each term in $2 Y = \frac{3 X}{4} - 1$ by $2$ .

$\frac{2 Y}{2} = \frac{\frac{3 X}{4}}{2} + \frac{- 1}{2}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $2$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{2 Y}{2} = \frac{\frac{3 X}{4}}{2} + \frac{- 1}{2}$

Step 4.3.2.1.2

Divide $Y$ by $1$ .

$Y = \frac{\frac{3 X}{4}}{2} + \frac{- 1}{2}$

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

Multiply the numerator by the reciprocal of the denominator.

$Y = \frac{3 X}{4} \cdot \frac{1}{2} + \frac{- 1}{2}$

Step 4.3.3.1.2

Multiply $\frac{3 X}{4} \cdot \frac{1}{2}$ .

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Step 4.3.3.1.2.1

Multiply $\frac{3 X}{4}$ by $\frac{1}{2}$ .

$Y = \frac{3 X}{4 \cdot 2} + \frac{- 1}{2}$

Step 4.3.3.1.2.2

Multiply $4$ by $2$ .

$Y = \frac{3 X}{8} + \frac{- 1}{2}$

Step 4.3.3.1.3

Move the negative in front of the fraction.

$Y = \frac{3 X}{8} - \frac{1}{2}$

Step 5

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

$2 Y - 2 = \frac{3}{4} \cdot (X - 4)$

Step 6

Solve the equation for $y$ .

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Step 6.1

Simplify $\frac{3}{4} \cdot (X - 4)$ .

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Step 6.1.1

Rewrite.

$2 Y - 2 = 0 + 0 + \frac{3}{4} \cdot (X - 4)$

Step 6.1.2

Simplify by adding zeros.

$2 Y - 2 = \frac{3}{4} \cdot (X - 4)$

Step 6.1.3

Apply the distributive property.

$2 Y - 2 = \frac{3}{4} X + \frac{3}{4} \cdot - 4$

Step 6.1.4

Combine $\frac{3}{4}$ and $X$ .

$2 Y - 2 = \frac{3 X}{4} + \frac{3}{4} \cdot - 4$

Step 6.1.5

Cancel the common factor of $4$ .

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Step 6.1.5.1

Factor $4$ out of $- 4$ .

$2 Y - 2 = \frac{3 X}{4} + \frac{3}{4} \cdot (4 (- 1))$

Step 6.1.5.2

Cancel the common factor.

$2 Y - 2 = \frac{3 X}{4} + \frac{3}{4} \cdot (4 \cdot - 1)$

Step 6.1.5.3

Rewrite the expression.

$2 Y - 2 = \frac{3 X}{4} + 3 \cdot - 1$

Step 6.1.6

Multiply $3$ by $- 1$ .

$2 Y - 2 = \frac{3 X}{4} - 3$

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.

$2 Y = \frac{3 X}{4} - 3 + 2$

Step 6.2.2

Add $- 3$ and $2$ .

$2 Y = \frac{3 X}{4} - 1$

Step 6.3

Divide each term in $2 Y = \frac{3 X}{4} - 1$ by $2$ and simplify.

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Step 6.3.1

Divide each term in $2 Y = \frac{3 X}{4} - 1$ by $2$ .

$\frac{2 Y}{2} = \frac{\frac{3 X}{4}}{2} + \frac{- 1}{2}$

Step 6.3.2

Simplify the left side.

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Step 6.3.2.1

Cancel the common factor of $2$ .

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Step 6.3.2.1.1

Cancel the common factor.

$\frac{2 Y}{2} = \frac{\frac{3 X}{4}}{2} + \frac{- 1}{2}$

Step 6.3.2.1.2

Divide $Y$ by $1$ .

$Y = \frac{\frac{3 X}{4}}{2} + \frac{- 1}{2}$

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

Multiply the numerator by the reciprocal of the denominator.

$Y = \frac{3 X}{4} \cdot \frac{1}{2} + \frac{- 1}{2}$

Step 6.3.3.1.2

Multiply $\frac{3 X}{4} \cdot \frac{1}{2}$ .

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Step 6.3.3.1.2.1

Multiply $\frac{3 X}{4}$ by $\frac{1}{2}$ .

$Y = \frac{3 X}{4 \cdot 2} + \frac{- 1}{2}$

Step 6.3.3.1.2.2

Multiply $4$ by $2$ .

$Y = \frac{3 X}{8} + \frac{- 1}{2}$

Step 6.3.3.1.3

Move the negative in front of the fraction.

$Y = \frac{3 X}{8} - \frac{1}{2}$

Step 7

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

$2 Y - 2 = \frac{3}{4} \cdot (X - 4)$

Step 8

Solve the equation for $y$ .

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Step 8.1

Simplify $\frac{3}{4} \cdot (X - 4)$ .

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Step 8.1.1

Rewrite.

$2 Y - 2 = 0 + 0 + \frac{3}{4} \cdot (X - 4)$

Step 8.1.2

Simplify by adding zeros.

$2 Y - 2 = \frac{3}{4} \cdot (X - 4)$

Step 8.1.3

Apply the distributive property.

$2 Y - 2 = \frac{3}{4} X + \frac{3}{4} \cdot - 4$

Step 8.1.4

Combine $\frac{3}{4}$ and $X$ .

$2 Y - 2 = \frac{3 X}{4} + \frac{3}{4} \cdot - 4$

Step 8.1.5

Cancel the common factor of $4$ .

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Step 8.1.5.1

Factor $4$ out of $- 4$ .

$2 Y - 2 = \frac{3 X}{4} + \frac{3}{4} \cdot (4 (- 1))$

Step 8.1.5.2

Cancel the common factor.

$2 Y - 2 = \frac{3 X}{4} + \frac{3}{4} \cdot (4 \cdot - 1)$

Step 8.1.5.3

Rewrite the expression.

$2 Y - 2 = \frac{3 X}{4} + 3 \cdot - 1$

Step 8.1.6

Multiply $3$ by $- 1$ .

$2 Y - 2 = \frac{3 X}{4} - 3$

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.

$2 Y = \frac{3 X}{4} - 3 + 2$

Step 8.2.2

Add $- 3$ and $2$ .

$2 Y = \frac{3 X}{4} - 1$

Step 8.3

Divide each term in $2 Y = \frac{3 X}{4} - 1$ by $2$ and simplify.

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Step 8.3.1

Divide each term in $2 Y = \frac{3 X}{4} - 1$ by $2$ .

$\frac{2 Y}{2} = \frac{\frac{3 X}{4}}{2} + \frac{- 1}{2}$

Step 8.3.2

Simplify the left side.

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Step 8.3.2.1

Cancel the common factor of $2$ .

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Step 8.3.2.1.1

Cancel the common factor.

$\frac{2 Y}{2} = \frac{\frac{3 X}{4}}{2} + \frac{- 1}{2}$

Step 8.3.2.1.2

Divide $Y$ by $1$ .

$Y = \frac{\frac{3 X}{4}}{2} + \frac{- 1}{2}$

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

Multiply the numerator by the reciprocal of the denominator.

$Y = \frac{3 X}{4} \cdot \frac{1}{2} + \frac{- 1}{2}$

Step 8.3.3.1.2

Multiply $\frac{3 X}{4} \cdot \frac{1}{2}$ .

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Step 8.3.3.1.2.1

Multiply $\frac{3 X}{4}$ by $\frac{1}{2}$ .

$Y = \frac{3 X}{4 \cdot 2} + \frac{- 1}{2}$

Step 8.3.3.1.2.2

Multiply $4$ by $2$ .

$Y = \frac{3 X}{8} + \frac{- 1}{2}$

Step 8.3.3.1.3

Move the negative in front of the fraction.

$Y = \frac{3 X}{8} - \frac{1}{2}$

Step 9

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

$2 Y - 2 = \frac{3}{4} \cdot (X - 4)$

Step 10

Solve the equation for $y$ .

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Step 10.1

Simplify $\frac{3}{4} \cdot (X - 4)$ .

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Step 10.1.1

Rewrite.

$2 Y - 2 = 0 + 0 + \frac{3}{4} \cdot (X - 4)$

Step 10.1.2

Simplify by adding zeros.

$2 Y - 2 = \frac{3}{4} \cdot (X - 4)$

Step 10.1.3

Apply the distributive property.

$2 Y - 2 = \frac{3}{4} X + \frac{3}{4} \cdot - 4$

Step 10.1.4

Combine $\frac{3}{4}$ and $X$ .

$2 Y - 2 = \frac{3 X}{4} + \frac{3}{4} \cdot - 4$

Step 10.1.5

Cancel the common factor of $4$ .

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Step 10.1.5.1

Factor $4$ out of $- 4$ .

$2 Y - 2 = \frac{3 X}{4} + \frac{3}{4} \cdot (4 (- 1))$

Step 10.1.5.2

Cancel the common factor.

$2 Y - 2 = \frac{3 X}{4} + \frac{3}{4} \cdot (4 \cdot - 1)$

Step 10.1.5.3

Rewrite the expression.

$2 Y - 2 = \frac{3 X}{4} + 3 \cdot - 1$

Step 10.1.6

Multiply $3$ by $- 1$ .

$2 Y - 2 = \frac{3 X}{4} - 3$

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.

$2 Y = \frac{3 X}{4} - 3 + 2$

Step 10.2.2

Add $- 3$ and $2$ .

$2 Y = \frac{3 X}{4} - 1$

Step 10.3

Divide each term in $2 Y = \frac{3 X}{4} - 1$ by $2$ and simplify.

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Step 10.3.1

Divide each term in $2 Y = \frac{3 X}{4} - 1$ by $2$ .

$\frac{2 Y}{2} = \frac{\frac{3 X}{4}}{2} + \frac{- 1}{2}$

Step 10.3.2

Simplify the left side.

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Step 10.3.2.1

Cancel the common factor of $2$ .

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Step 10.3.2.1.1

Cancel the common factor.

$\frac{2 Y}{2} = \frac{\frac{3 X}{4}}{2} + \frac{- 1}{2}$

Step 10.3.2.1.2

Divide $Y$ by $1$ .

$Y = \frac{\frac{3 X}{4}}{2} + \frac{- 1}{2}$

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

Multiply the numerator by the reciprocal of the denominator.

$Y = \frac{3 X}{4} \cdot \frac{1}{2} + \frac{- 1}{2}$

Step 10.3.3.1.2

Multiply $\frac{3 X}{4} \cdot \frac{1}{2}$ .

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Step 10.3.3.1.2.1

Multiply $\frac{3 X}{4}$ by $\frac{1}{2}$ .

$Y = \frac{3 X}{4 \cdot 2} + \frac{- 1}{2}$

Step 10.3.3.1.2.2

Multiply $4$ by $2$ .

$Y = \frac{3 X}{8} + \frac{- 1}{2}$

Step 10.3.3.1.3

Move the negative in front of the fraction.

$Y = \frac{3 X}{8} - \frac{1}{2}$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & \frac{3 X}{8} - \frac{1}{2} \\ - 1 & \frac{3 X}{8} - \frac{1}{2} \\ 0 & \frac{3 X}{8} - \frac{1}{2} \\ 1 & \frac{3 X}{8} - \frac{1}{2} \\ 2 & \frac{3 X}{8} - \frac{1}{2} \end{array}$

Step 12