Find the Parallel Line y=-2x-6 , P=(4,6)

$y = - 2 x - 6$ , $P = (4, 6)$

Step 1

Use the slope-intercept form to find the slope.

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

$y = m x + b$

Using the slope-intercept form, the slope is $- 2$ .

$m = - 2$

Step 2

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

Step 3

Use the slope $- 2$ and a given point $P = (4, 6)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (6) = - 2 \cdot (x - (4))$

Step 4

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

$y - 6 = - 2 \cdot (x - 4)$

Step 5

Solve for $y$ .

Simplify $- 2 \cdot (x - 4)$ .

Rewrite.

$y - 6 = 0 + 0 - 2 \cdot (x - 4)$

Simplify by adding zeros.

$y - 6 = - 2 \cdot (x - 4)$

Apply the distributive property.

$y - 6 = - 2 x - 2 \cdot - 4$

Multiply $- 2$ by $- 4$ .

$y - 6 = - 2 x + 8$

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

Add $6$ to both sides of the equation.

$y = - 2 x + 8 + 6$

Add $8$ and $6$ .

$y = - 2 x + 14$

Step 6

Find the Parallel Line y=-2x-6 , P=(4,6)

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