What is the slope of any line perpendicular to the line passing through #(0,2)# and #(3,15)#?

1 Answer
Aug 2, 2018

Answer:

The slope of any line passing through the given two points is #-3/13#.

Explanation:

First find the slope of the line passing through the two given points.

#m=(y_2-y_1)/(x_2-x_1)#,

where:

#m# is the slope, and #(x_1,y_1)# and #(x_2,y_2)# are the two given points. I'm going to use point #(0,2)# as #(x_1,y_1)# and #(3,15)# as #(x_2,y_2)#. You could do the reverse and you would get the same slope.

Plug in the known values and solve for slope.

#m=(15-2)/(3-0)#

#m=13/3#

The perpendicular slope of any line is the negative reciprocal of the original slope, so that #m_1m_2=-1#.

#13/3xx-3/13=-39/39=-1#. The perpendicular slope is #-3/13#.

graph{(y+13/3x)(y-3/13x)=0 [-10, 10, -5, 5]}