Math CentralQuandaries & Queries


Question from Mykolyn, a student:

How do you find the slope of a line that is perpendicular to the graph of:
y= -1/2x+4?

We have two responses for you.


Hi there,

If two lines are perpendicular to each other, their slopes are negative reciprocals of each other.  This results in their product being -1 if multiplied together.

Ex.  2/3 and -3/2 are negative reciprocals of each other
       -3 and 1/3 and 4 and -1/4 are also negative reciprocals involving integer values and their

The line you were given was written in slope-intercept or y=mx+b form where m is the slope, so the coefficient on x in the equation (-1/2) is the slope of the line given to you.

Since the perpendicular line must have a slope that is the negative reciprocal of -1/2, you should now be able to determine its slope.

Hope this helps,



Hi Mykolyn,

To find the slope of a perpendicular line, you take the slope you are
given and find the negative reciprocal of it.  The rest of the
equation is the same.

For example, if you're asked to find the slope of the line that is
perpendicular to the line with equation y = 2/3x+4, first you need to
determine what the slope of that line is.  The form of the equation is
y = mx + b, where m is the slope and b is the y-intercept.  So we know
2/3 is the slope.  To take the negative reciprocal (to find the
perpendicular slope), you simply flip the number so it becomes 3/2
and multiply by a negative.  Therefore, you're new slope is -3/2 and
the equation of the perpendicular line is y= -3/2x + 4.

Sara Ulmer

About Math Central


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.
Quandaries & Queries page Home page University of Regina PIMS