Algebra Examples

$y - 2 x = - 8 (x - 8)$ , $(6, - 6)$

Step 1

Rewrite in slope-intercept form.

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Step 1.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 1.2

Simplify the right side.

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Step 1.2.1

Simplify $- 8 (x - 8)$ .

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Step 1.2.1.1

Apply the distributive property.

$y - 2 x = - 8 x - 8 \cdot - 8$

Step 1.2.1.2

Multiply $- 8$ by $- 8$ .

$y - 2 x = - 8 x + 64$

Step 1.3

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

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Step 1.3.1

Add $2 x$ to both sides of the equation.

$y = - 8 x + 64 + 2 x$

Step 1.3.2

Add $- 8 x$ and $2 x$ .

$y = - 6 x + 64$

Step 2

Using the slope-intercept form, the slope is $- 6$ .

$m = - 6$

Step 3

To find an equation that is parallel, the slopes must be equal. Find the parallel line using the point-slope formula.

Step 4

Use the slope $- 6$ and a given point $(6, - 6)$ to substitute for $x_{1}$ and $y_{1}$ in the point-slope form $y - y_{1} = m (x - x_{1})$ , which is derived from the slope equation $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (- 6) = - 6 \cdot (x - (6))$

Step 5

Simplify the equation and keep it in point-slope form.

$y + 6 = - 6 \cdot (x - 6)$

Step 6

Solve for $y$ .

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Step 6.1

Simplify $- 6 \cdot (x - 6)$ .

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Step 6.1.1

Rewrite.

$y + 6 = 0 + 0 - 6 \cdot (x - 6)$

Step 6.1.2

Simplify by adding zeros.

$y + 6 = - 6 \cdot (x - 6)$

Step 6.1.3

Apply the distributive property.

$y + 6 = - 6 x - 6 \cdot - 6$

Step 6.1.4

Multiply $- 6$ by $- 6$ .

$y + 6 = - 6 x + 36$

Step 6.2

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

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Step 6.2.1

Subtract $6$ from both sides of the equation.

$y = - 6 x + 36 - 6$

Step 6.2.2

Subtract $6$ from $36$ .

$y = - 6 x + 30$

Step 7