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

Question 120587: find the slope of any line perpendicular to the line through points (0,5) and
(-3,-4)
Answer by solver91311(24713) (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.

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, (,).

Then the equation for the line becomes:

And then a little arithmetic to get:

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

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 is perpendicular to line if and only if slope is the negative reciprocal of slope , that is:

All we need now is the negative reciprocal of 3, namely
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