Compare the rates of change of the following 2 items? Item 1:# y=-2x+6 color(white)("d")# Item 2: A line which passes through the points (2,2) and (1,6)

Which of the following is correct:
#color(white)("d")# A. The items decrease at the same rate. #color(white)("d")# B. Item 1 decreases faster.#color(white)("d")# C. Item 2 decreases faster.

1 Answer
May 14, 2018

Option C is true.

Explanation:

To enable direct comparison we need to convert the given 2 points into the gradient of an equation.

Standard form #y=mx+c# where #m# is the gradient.

Gradient is #("change in y")/("change in x") -> (y_2-y_1)/(x_2-x_1) #

Note that #x_1# is the least #x# value. So we travel from #x=1" to "x=2#

Thus #(x_1,y_1)=(1,6) and (x_2,y_2)=(2,2)# giving:

#m=(y_2-y_1)/(x_2-x_1) =(2-6)/(2-1) = (-4)/1#

The slope of the given equation is #-2 larr #Item 1
The slope between the given points is #-4larr# Item 2
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Options given:

A: Items decrease at the same rate #color(red)(larr" False")#
B: Item 1 decreases faster #color(white)("ddddd.d")color(red)(larr" False")#
C: Item 2 decreases faster #color(white)("ddddddd")color(green)(larr" True")#