What is the equation of the line perpendicular to #y=9/20x # that passes through # (-1,-5) #?

1 Answer
OddJerbb · Hriman
Apr 27, 2018

Find the negative reciprocal of the slope of our given equation,
#y=9/20x#.

Keep in mind that the slope of any line is defined as the negative reciprocal of the slope of the line that it is perpendicular to.

The negative reciprocal of #9/20# is #-20/9#. This is the slope of our perpendicular line.

This perpendicular line also lies on the point (-1, -5). With the coordinates of this point and the slope we previously found, we can construct our answer in point slope form:

#y-y_1 = m(x-x_1)#, where m = slope, #x_1# and #y_1# are the x and y-coordinate of the point (#x_1#, #y_1#) respectively.

In our case, m = #-20/9#, #x_1# = -1, and #y_1# = -5.

Now all we must do is to simply plug in our values:
#y+5=-20/9(x+1)#

If the question requires an equation in slope-intercept form, simply subtract 5 from both sides and simplify!

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