Pre-Algebra Examples

$y - 8 = (\frac{1}{8}) (x - 6)$

Step 1

The standard form of a linear equation is $A x + B y = C$ .

Step 2

Multiply both sides by $8$ .

$8 (y - 8) = 8 (\frac{1}{8} (x - 6))$

Step 3

Simplify the left side.

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Step 3.1

Simplify $8 (y - 8)$ .

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Step 3.1.1

Apply the distributive property.

$8 y + 8 \cdot - 8 = 8 (\frac{1}{8} (x - 6))$

Step 3.1.2

Multiply $8$ by $- 8$ .

$8 y - 64 = 8 (\frac{1}{8} (x - 6))$

Step 4

Simplify the right side.

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Step 4.1

Simplify $8 (\frac{1}{8} (x - 6))$ .

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Step 4.1.1

Apply the distributive property.

$8 y - 64 = 8 (\frac{1}{8} x + \frac{1}{8} \cdot - 6)$

Step 4.1.2

Combine $\frac{1}{8}$ and $x$ .

$8 y - 64 = 8 (\frac{x}{8} + \frac{1}{8} \cdot - 6)$

Step 4.1.3

Cancel the common factor of $2$ .

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Step 4.1.3.1

Factor $2$ out of $8$ .

$8 y - 64 = 8 (\frac{x}{8} + \frac{1}{2 (4)} \cdot - 6)$

Step 4.1.3.2

Factor $2$ out of $- 6$ .

$8 y - 64 = 8 (\frac{x}{8} + \frac{1}{2 \cdot 4} \cdot (2 \cdot - 3))$

Step 4.1.3.3

Cancel the common factor.

$8 y - 64 = 8 (\frac{x}{8} + \frac{1}{2 \cdot 4} \cdot (2 \cdot - 3))$

Step 4.1.3.4

Rewrite the expression.

$8 y - 64 = 8 (\frac{x}{8} + \frac{1}{4} \cdot - 3)$

Step 4.1.4

Combine $\frac{1}{4}$ and $- 3$ .

$8 y - 64 = 8 (\frac{x}{8} + \frac{- 3}{4})$

Step 4.1.5

Move the negative in front of the fraction.

$8 y - 64 = 8 (\frac{x}{8} - \frac{3}{4})$

Step 4.1.6

Apply the distributive property.

$8 y - 64 = 8 \frac{x}{8} + 8 (- \frac{3}{4})$

Step 4.1.7

Cancel the common factor of $8$ .

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Step 4.1.7.1

Cancel the common factor.

$8 y - 64 = 8 \frac{x}{8} + 8 (- \frac{3}{4})$

Step 4.1.7.2

Rewrite the expression.

$8 y - 64 = x + 8 (- \frac{3}{4})$

Step 4.1.8

Cancel the common factor of $4$ .

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Step 4.1.8.1

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$8 y - 64 = x + 8 (\frac{- 3}{4})$

Step 4.1.8.2

Factor $4$ out of $8$ .

$8 y - 64 = x + 4 (2) \frac{- 3}{4}$

Step 4.1.8.3

Cancel the common factor.

$8 y - 64 = x + 4 \cdot 2 \frac{- 3}{4}$

Step 4.1.8.4

Rewrite the expression.

$8 y - 64 = x + 2 \cdot - 3$

Step 4.1.9

Multiply $2$ by $- 3$ .

$8 y - 64 = x - 6$

Step 5

Rewrite the equation.

$x - 6 = 8 y - 64$

Step 6

Move all terms containing variables to the left side of the equation.

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Step 6.1

Subtract $8 y$ from both sides of the equation.

$x - 6 - 8 y = - 64$

Step 6.2

Move $- 6$ .

$x - 8 y - 6 = - 64$

Step 7

Move all terms not containing a variable to the right side of the equation.

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Step 7.1

Add $6$ to both sides of the equation.

$x - 8 y = - 64 + 6$

Step 7.2

Add $- 64$ and $6$ .

$x - 8 y = - 58$

Step 8