Question

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

Answer 1

Answer:

$y - 9 = \frac{1}{2}(x +3)$

Step-by-step 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

$m_2 =\frac{ -1}{-2}$

$m_2 =\frac{1}{2}$

The point slope form of a line is;

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

Where $(x_1,y_1) = (-3,9)$ and $m_2 =\frac{1}{2}$

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

$y - 9 = \frac{1}{2}(x - (-3))$

Open the inner bracket

$y - 9 = \frac{1}{2}(x +3)$

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

$y - 9 = \frac{1}{2}(x +3)$