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)

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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)

If the line is perpendicular, then as a rule the gradient of the perpendicular line will be the negative inverse of the gradient of the line given.

Therefore the gradient of the perpendicular line would be 1/2

so now just substitute in the equation of a line (y=mx+c) where y and x are given by -3 and 9, and your new m=1/2

Hope this helps

The answer is A because the slope is -2 and that is the only one that shows -2 as a slope

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

Step-by-step explanation:

For the equation y = -2x + 8, your slope, m, is -2. To find the slope for a line perpendicular to the original line, we do the opposite reciprocal of this number. The slope of the perpendicular line is 1/2.

Point-slope form is: y - y1 = m(x - x1) where x1 and y1 are the x- and y-coordinates of an ordered pair.

With this new slope for the perpendicular line, and the point we are given, we just plug in the info.

Your equation is: y - 9 = 1/2(x + 3)

[tex]y - 9 = \frac{1}{2}(x +3)[/tex]

Step-by-step explanation:

Given

Function; [tex]y = -2x + 8[/tex]

Required

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

First, we need to determine the slope of: [tex]y = -2x + 8[/tex]

The slope intercept of an equation is in form;

[tex]y = mx + b[/tex]

Where m represent the slope

Comparing [tex]y = m_1x + b[/tex] to [tex]y = -2x + 8[/tex];

We'll have that

[tex]m_1 = -2[/tex]

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

The condition for parallel line is;

[tex]m_1 * m_2 = -1[/tex]

Substitute [tex]m_1 = -2[/tex]

[tex](-2) * m_2 = -1[/tex]

Divide both sides by -2

[tex]m_2 =\frac{ -1}{-2}[/tex]

[tex]m_2 =\frac{1}{2}[/tex]

The point slope form of a line is;

[tex]y - y_1 = m_2(x - x_1)[/tex]

Where [tex](x_1,y_1) = (-3,9)[/tex] and [tex]m_2 =\frac{1}{2}[/tex]

[tex]y - y_1 = m_2(x - x_1)[/tex]becomes

[tex]y - 9 = \frac{1}{2}(x - (-3))[/tex]

Open the inner bracket

[tex]y - 9 = \frac{1}{2}(x +3)[/tex]

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

[tex]y - 9 = \frac{1}{2}(x +3)[/tex]

For this case we have the following linear equation:

[tex]y = -2x + 8 [/tex]

As the lines are perpendicular, then the slope of the line is:

[tex]m' = \frac{-1}{m}[/tex]

Where,

m: is the slope of the original line

Substituting values we have:

[tex]m' = \frac{-1}{-2}[/tex]

Rewriting:

[tex]m' = \frac{1}{2}[/tex]

Then, the equation in point-slope form is given by:

[tex]y-yo = m '(x-xo) [/tex]

Where,

(xo, yo): ordered pair that goes through the line.

Substituting values we have:

[tex]y-9 = \frac{1}{2}(x+3) [/tex]

an equation in point-slope form for the line perpendicular to y = –2x + 8 that passes through (–3, 9) is:

[tex]y-9 = \frac{1}{2}(x+3)[/tex]

A

-2 is the slope which goes after the equal sign