Find the Parallel Line y=2x-11 , P=(3,12)

$y = 2 x - 11$ , $P = (3, 12)$

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 $P = (3, 12)$ 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 $m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ .

$y - (12) = 2 \cdot (x - (3))$

Step 4

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

$y - 12 = 2 \cdot (x - 3)$

Step 5

Solve for $y$ .

Simplify $2 \cdot (x - 3)$ .

Rewrite.

$y - 12 = 0 + 0 + 2 \cdot (x - 3)$

Simplify by adding zeros.

$y - 12 = 2 \cdot (x - 3)$

Apply the distributive property.

$y - 12 = 2 x + 2 \cdot - 3$

Multiply $2$ by $- 3$ .

$y - 12 = 2 x - 6$

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

Add $12$ to both sides of the equation.

$y = 2 x - 6 + 12$

Add $- 6$ and $12$ .

$y = 2 x + 6$

Step 6

Find the Parallel Line y=2x-11 , P=(3,12)

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