Calculus Examples

$y - (- \frac{1}{4}) = - \frac{1}{32} \cdot (x - (- 8))$

Step 1

Simplify $- \frac{1}{32} \cdot (x - (- 8))$ .

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Step 1.1

Rewrite.

$y + \frac{1}{4} = 0 + 0 - \frac{1}{32} \cdot (x - (- 8))$

Step 1.2

Multiply $- 1$ by $- 8$ .

$y + \frac{1}{4} = - \frac{1}{32} \cdot (x + 8)$

Step 1.3

Apply the distributive property.

$y + \frac{1}{4} = - \frac{1}{32} x - \frac{1}{32} \cdot 8$

Step 1.4

Combine $x$ and $\frac{1}{32}$ .

$y + \frac{1}{4} = - \frac{x}{32} - \frac{1}{32} \cdot 8$

Step 1.5

Cancel the common factor of $8$ .

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Step 1.5.1

Move the leading negative in $- \frac{1}{32}$ into the numerator.

$y + \frac{1}{4} = - \frac{x}{32} + \frac{- 1}{32} \cdot 8$

Step 1.5.2

Factor $8$ out of $32$ .

$y + \frac{1}{4} = - \frac{x}{32} + \frac{- 1}{8 (4)} \cdot 8$

Step 1.5.3

Cancel the common factor.

$y + \frac{1}{4} = - \frac{x}{32} + \frac{- 1}{8 \cdot 4} \cdot 8$

Step 1.5.4

Rewrite the expression.

$y + \frac{1}{4} = - \frac{x}{32} + \frac{- 1}{4}$

Step 1.6

Move the negative in front of the fraction.

$y + \frac{1}{4} = - \frac{x}{32} - \frac{1}{4}$

Step 2

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

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Step 2.1

Subtract $\frac{1}{4}$ from both sides of the equation.

$y = - \frac{x}{32} - \frac{1}{4} - \frac{1}{4}$

Step 2.2

Combine the numerators over the common denominator.

$y = \frac{- x}{32} + \frac{- 1 - 1}{4}$

Step 2.3

Subtract $1$ from $- 1$ .

$y = \frac{- x}{32} + \frac{- 2}{4}$

Step 2.4

Simplify each term.

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Step 2.4.1

Move the negative in front of the fraction.

$y = - \frac{x}{32} + \frac{- 2}{4}$

Step 2.4.2

Cancel the common factor of $- 2$ and $4$ .

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Step 2.4.2.1

Factor $2$ out of $- 2$ .

$y = - \frac{x}{32} + \frac{2 (- 1)}{4}$

Step 2.4.2.2

Cancel the common factors.

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Step 2.4.2.2.1

Factor $2$ out of $4$ .

$y = - \frac{x}{32} + \frac{2 \cdot - 1}{2 \cdot 2}$

Step 2.4.2.2.2

Cancel the common factor.

$y = - \frac{x}{32} + \frac{2 \cdot - 1}{2 \cdot 2}$

Step 2.4.2.2.3

Rewrite the expression.

$y = - \frac{x}{32} + \frac{- 1}{2}$

Step 2.4.3

Move the negative in front of the fraction.

$y = - \frac{x}{32} - \frac{1}{2}$