Question

What is the slope of the line perpendicular to this line: y=2x-3?

Answer 1

Any line with the slope of `-1/2` will be perpendicular to the given line.

Explanation:

`y = 2x -3` has a slope of `+ 2`, which means the line goes over `1` to the right and up `2` ( a positive slope). The inverse of 2 = 1/2 and the line must have a negative slope so the slope must be - 1/2. The y intercept of -3 does not matter. Any line with the slope of -1/2 will intercept the line at 90 degrees. y= - 1/2 + (x) is the answer.

Note that product of slopes of two perpendicular lines is always `-1`. An example is given below.

graph{(y-2x+3)(2y+x+3)=0 [-10, 10, -5, 5]}