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

Jul 29, 2016

Any line with the slope of $- \frac{1}{2}$ will be perpendicular to the given line.
$y = 2 x - 3$ 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.