Finite Math Examples

$y - 2 = - \frac{1}{3} \cdot (x - 1)$

Step 1

Rewrite the equation as $- \frac{1}{3} \cdot (x - 1) = y - 2$ .

$- \frac{1}{3} \cdot (x - 1) = y - 2$

Step 2

Multiply both sides of the equation by $- 3$ .

$- 3 (- \frac{1}{3} \cdot (x - 1)) = - 3 (y - 2)$

Step 3

Simplify both sides of the equation.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $- 3 (- \frac{1}{3} \cdot (x - 1))$ .

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Step 3.1.1.1

Apply the distributive property.

$- 3 (- \frac{1}{3} x - \frac{1}{3} \cdot - 1) = - 3 (y - 2)$

Step 3.1.1.2

Combine $x$ and $\frac{1}{3}$ .

$- 3 (- \frac{x}{3} - \frac{1}{3} \cdot - 1) = - 3 (y - 2)$

Step 3.1.1.3

Multiply $- \frac{1}{3} \cdot - 1$ .

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Step 3.1.1.3.1

Multiply $- 1$ by $- 1$ .

$- 3 (- \frac{x}{3} + 1 (\frac{1}{3})) = - 3 (y - 2)$

Step 3.1.1.3.2

Multiply $\frac{1}{3}$ by $1$ .

$- 3 (- \frac{x}{3} + \frac{1}{3}) = - 3 (y - 2)$

Step 3.1.1.4

Apply the distributive property.

$- 3 (- \frac{x}{3}) - 3 (\frac{1}{3}) = - 3 (y - 2)$

Step 3.1.1.5

Cancel the common factor of $3$ .

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Step 3.1.1.5.1

Move the leading negative in $- \frac{x}{3}$ into the numerator.

$- 3 \frac{- x}{3} - 3 (\frac{1}{3}) = - 3 (y - 2)$

Step 3.1.1.5.2

Factor $3$ out of $- 3$ .

$3 (- 1) \frac{- x}{3} - 3 (\frac{1}{3}) = - 3 (y - 2)$

Step 3.1.1.5.3

Cancel the common factor.

$3 \cdot - 1 \frac{- x}{3} - 3 (\frac{1}{3}) = - 3 (y - 2)$

Step 3.1.1.5.4

Rewrite the expression.

$- - x - 3 (\frac{1}{3}) = - 3 (y - 2)$

Step 3.1.1.6

Multiply.

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Step 3.1.1.6.1

Multiply $- 1$ by $- 1$ .

$1 x - 3 (\frac{1}{3}) = - 3 (y - 2)$

Step 3.1.1.6.2

Multiply $x$ by $1$ .

$x - 3 (\frac{1}{3}) = - 3 (y - 2)$

Step 3.1.1.7

Cancel the common factor of $3$ .

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Step 3.1.1.7.1

Factor $3$ out of $- 3$ .

$x + 3 (- 1) \frac{1}{3} = - 3 (y - 2)$

Step 3.1.1.7.2

Cancel the common factor.

$x + 3 \cdot - 1 \frac{1}{3} = - 3 (y - 2)$

Step 3.1.1.7.3

Rewrite the expression.

$x - 1 = - 3 (y - 2)$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $- 3 (y - 2)$ .

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Step 3.2.1.1

Apply the distributive property.

$x - 1 = - 3 y - 3 \cdot - 2$

Step 3.2.1.2

Multiply $- 3$ by $- 2$ .

$x - 1 = - 3 y + 6$

Step 4

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

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Step 4.1

Add $1$ to both sides of the equation.

$x = - 3 y + 6 + 1$

Step 4.2

Add $6$ and $1$ .

$x = - 3 y + 7$