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

1 Answer

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


#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]}