Question

Find the slope of a line perpendicular to y=-2/5x+4/5.

Answer 1

For two lines to be perpendicular their slopes must be negative reciprocals of one another, mathematically:

m1*m2=-1

In this case, our reference line has a slope of -2/5 so our perpendicular slope must satisfy:

-2m/5=-1

-2m=-5

m=-5/-2

m=5/2

....

The negative reciprocal property can be more easily understood by realizing that the angle of a line is:

tanα=m

α=arctanm

So if one line, A, has a slope of m and the other, B, has a slope of -1/m

A=arctan m, B=arctan -1/m

B-A=90°  (feel free to use any value for m that you choose to see that this is true, so if the two lines differ by 90°, they are indeed perpendicular)