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# Which of the following equations represents a line that is perpendicular to the line that passes through the points below?

Which of the following equations represents a line that is perpendicular to the line that passes through the points below?
(-8,-5) (-6,3)

### 3 Answers by Expert Tutors

William S. | Experienced scientist, mathematician and instructor - WilliamExperienced scientist, mathematician and...
4.4 4.4 (10 lesson ratings) (10)
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Given the points ((-8, -5) and (-6, 3)

the slope, m, of the line on which these points lie is

(-5 - 3)/[-8 -(-6)] = (-8)/(-2) = 4

The complete equation of the line is

y = 4x + b

We can solve for b by substituting one of the points into this equation:

3 = (4)(-6) + b

b = 27

Check

Does 27 = -5 - 4(-8)?

YES!!!!

The equation of any line perpendicular to y = 4x + 27 will have the general form y = (-x/4) + b

The slope of any line perpendicular to this will be (-1/4)
Amarjeet K. | Professional Engineer for Math and Science TuroringProfessional Engineer for Math and Scien...
4.6 4.6 (8 lesson ratings) (8)
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slope of given line = (3-(-5))/(-6 -(-8)) = 8/2 = 4

Slope of perpendicular line = -1/4

Equation of the perpendicular line

y = mx + b

y = -1/4x + b
Vivian L. | Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACHMicrosoft Word/Excel/Outlook, essay comp...
3.0 3.0 (1 lesson ratings) (1)
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Hi Derp;
Let's begin with the points...
(-8,-5) (-6,3)
We need to establish slope, m.  This is the change-of-y divided by the change-of-x, also known as rise-over-run.
m=(y-y1)/(x-x1)
m=(-5-3)/(-8--6)
m=-8/(-8+6)
m=-8/-2
m=4
The line perpendicular has a slope of -1/4, the negative inverse.
y=(-1/4)x+b
b is the y-intercept, the value of y when x=0.  Because I do not have any points for this second line, I cannot establish this.