Question

Identify an equation in point-slope form for the line perpendicular to

y=-2x + 8 that passes through (-3,9).
O A. y - 9 =-2(x+3)
O B. y+3 (x-9)
O C. y-9 - (x+3)
O D. y + 9 = 2(x-3)

Answer 1

`y - 9 = (1)/(2)(x +3)`

Explanation:

Given

Function;
`y = -2x + 8`

Required

Find an equation perpendicular to the given function if it passes through (-3,9)

First, we need to determine the slope of:
`y = -2x + 8`

The slope intercept of an equation is in form;

`y = mx + b`

Where m represent the slope

Comparing
`y = m_1x + b` to
`y = -2x + 8`;

We'll have that

`m_1 = -2`

Going from there; we need to calculate the slope of the parallel line

The condition for parallel line is;

`m_1 * m_2 = -1`

Substitute
`m_1 = -2`

`(-2) * m_2 = -1`

Divide both sides by -2

`m_2 =( -1)/(-2)`

`m_2 =(1)/(2)`

The point slope form of a line is;

`y - y_1 = m_2(x - x_1)`

Where
`(x_1,y_1) = (-3,9)` and
`m_2 =(1)/(2)`

`y - y_1 = m_2(x - x_1)`becomes

`y - 9 = (1)/(2)(x - (-3))`

Open the inner bracket

`y - 9 = (1)/(2)(x +3)`

Hence, the point slope form of the perpendicular line is:

`y - 9 = (1)/(2)(x +3)`