Write an equation in point-slope form for the line through the given point (4,-6) with the given slope m=3/5?

2 Answers
Michael
Apr 3, 2015

#y=mx+c#

#-6=(4xx(3)/(5))+c#

#c=-12/5-6=-42/5#

So:

#y=(3)/(5)x-42/5#

Gió
Apr 3, 2015

The point slope form comes from the definition of slope as a measure of the change in #y# for a given change in #x# in passing from point 1 to point 2, i.e.:
slope#=m=(Deltay)/(Deltax)=(y_2-y_1)/(x_2-x_1)#...........(1).
The only difference here is that you do not have 2 points but only one!
So you have: the value of #m# and the coordinates of one point, say, point 1. So we can write in (1):
#3/5=(y-(-6))/(x-4)# where the coordinates of the other point are the unknown #x,y#.
You get rearranging:
#y+6=3/5(x-4)#
#y+6=3/5x-12/5#
#y=3/5x-12/5-6#
#y=3/5x-42/5#

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