What is the slope-intercept form of the line passing through #(2, 2) # and #(-1, 4) #?

1 Answer
Jun 1, 2016

Answer:

#-2/3# is the slope and #10/3# is the intercept.

Explanation:

A line in the plane follow the equation

#y=mx+q#. In this equation we want to calculate the two parameters #m# and #q#. To do it we substitute the values of #x# and #y# and we have a system of equations

#2=2m+q#
#4=-1m+q#

from one of the two equation (for example the first) I write one variable as the other:

#2=2m+q# then #q=2-2m#

and now substitute this in the other equation

#4=-m+q# then #4=-m+2-2m#
#4=2-3m#
#4-2=-3m#
#2=-3m#
#m=-2/3#

to find #q# I take the #q=2-2m# and substitute the value of #m#

#q=2-2(-2/3)=2+4/3=10/3#

The line has equation

#y=-2/3x+10/3# where #-2/3# is the slope and #10/3# is the intercept.