SOLUTION: find the slope of any line perpendicular to the line through points (0,5) and (-3,-4)

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Question 120587: find the slope of any line perpendicular to the line through points (0,5) and
(-3,-4)
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
Step 1: Find the equation of the line through (0,5) and (-3,-4). Use the two-point form of the line because you are given two points.

y-y%5B1%5D=%28%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29%29%28x-x%5B1%5D%29

It doesn't matter which point you call 1 and which you call 2 as long as you are consistent. Let's say (0,5) is point 1, (x%5B1%5D,y%5B1%5D).

Then the equation for the line becomes:

y-5=%28%28%28-4%29-5%29%2F%28-3-0%29%29%28x-0%29

And then a little arithmetic to get:

y-5=%28%28-9%29%2F%28-3%29%29x
y-5=3x

And then put the equation into slope-intercept form by solving for y,

y=3x%2B5

Now, by inspection of the coefficient on the x term, we can see that the slope of the line through the points is 3.

But we want the slope of a perpendicular line. The rule is that line L%5B1%5D is perpendicular to line L%5B2%5D if and only if slope m%5B1%5D is the negative reciprocal of slope m%5B2%5D, that is: m%5B1%5D=-1%2Fm%5B2%5D

All we need now is the negative reciprocal of 3, namely -1%2F3