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

Question

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

(-8,-5) (-6,3)

Answer 1

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)

Answer 2

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

Answer 3

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.