How do you find the slope of the secant lines of #f(x) = -3x + 2 # through the points: (-4,(f(-4)) and (1,f(1))?

1 Answer
Mar 1, 2016

#-3#

Explanation:

Find the points' #y#-values by evaluating #f(-4)# and #f(1)#:

#f(-4)=-3(-4)+2=12+2=14#

#f(1)=-3(1)+2=-3+2=-1#

The two points on the secant line are #(-4,14)# and #(1,-1)#.

The slope #m# can then be found using the slope equation:

#m=(Deltay)/(Deltax)=(14-(-1))/(-4-1)=15/(-5)=-3#

This should make sense, since #f(x)# is a line. The secant line, which passes through two points on #f(x)#, will have to be the exact same as #f(x)#--there's no other way a line can intercept two points.

Since the secant line is identical to #f(x)#, we can tell that they will have the same slope, and the slope of #f(x)=-3x+2# is #-3#.