What is the slope of any line perpendicular to the line passing through #(3,6)# and #(-8,4)#?

1 Answer
Feb 24, 2016

Answer:

#-11/2#

Explanation:

#color(magenta)("Introduction to how it works")#

Standard form of the equation of a straight line is: #y=mx+c#
Where #m# is the gradient (slope)

#color(green)("Any line perpendicular to the original line has the slope of: ")#
#color(green)( (-1)xx1/m)#

So for the second line the equation changes

#color(blue)("From ")color(brown)(y=mx+c )color(blue)(" to ")color(green)(y=-1/mx+c)#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(magenta)("Answering your question")#

#color(blue)("Determine the gradient of the given line")#
Let the first listed coordinates be the first point

#(x_1,y_1) -> (3,6)#
#(x_2,y_2)->(-8,4)#

Gradient given line#-> ("change in y-axis")/("change in x-axis left to right")#

Gradient given line (m)#->(y_2-y_1)/(x_2-x_1)->(4-6)/((-8)-3)->(-2)/(-11)=+2/11#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("Determine the gradient of the line perpendicular to the first one")#

#(-1)xx1/m = -11/2#