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

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3 Answers

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)
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
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.