Rate o f C hange
and Slope
Co m m o n Co r e St a t e St a n d a r d s
F-LE.A.1b Reco g n i ze si t u at i o n s i n w h i ch o n e q u an t i t y
changes at a const ant r at e per unit int erval relat ive t o
anot her. A lso F-IF.B.6
M P 1, M P 2, M P 3, M P 4Objectives To find rates of change from tables
To find slope~ ■» ~Drawing a diagram
may help.MATHEMATICAL
PRACTICES§ j Getting Ready!The table shows the horizontal and vertical
distances from the base o f the mountain a t
several poles along the path o f a ski lift. The
poles a re connected by cab le. Betw een which
tw o poles is th e cable's path th e steepest?
How do you know?X XHorizontal Vertical
Pole Distance Distancemm^2030
m^4035
wm^6060(^810070) • ....
Lesson
Vocabulary
rate o f change
slope
Essent ial Und er st and ing You can use ratios to show a relationship b etw een
changing quantities, such as vertical an d h orizontal change.
Rate of change shows th e relationship b etw een two changing quantities. W hen one
q uantity d ep e n d s on th e other, th e following is true.
change in the dependent variable
rate o c ange change in the independent variable
Think
Does this problem
look like one you've
seen before?
Yes. In Lesson 2-6, you
w rote rates and unit
rates. The rate of change
in Problem 1 is an
example o f a unit rate.
) F in d in g R a te o f C h a n g e U s in g a T a b le
Marching Band The table shows the distance a band marches
over time. Is the rate of change in distance with respect to
time constant? What does the rate of change represent?
change in distance
rate of change = — r b change in time;------
Calculate the rate of change from one row of the table to the next.
520 - 260 _ 260 780 - 520 260 1040 - 780
2 - 1
260
1
260
1 4-3
260
1
The rate of change is co n stan t an d equals It represents
th e distance the b a n d m arches p e r m inute.
Go t I t? 1. In Problem 1, do you get th e sam e rate of change if you use
nonconsecutive rows of the table? Explain.
Distance Marched
1 260
520
780
1040
294 Chapter 5 Linear Functions