Teacher Notes - Texas Instruments TI-83 Plus Manual Book

Chapter 3: Linear Functions
Linear Functions: Slope as Rate of Change
Objectives
To associate the slope of a straight line with a constant rate of change.
To calculate the rate of change from data points on a line, using the correct units.
To read from a linear graph: the rate of change, the scale of the axes, and the correct units.
Math Highlights
This section highlights the use of the slope formula to find the rate of change from graphs and
data. Students may need to review the slope formula; see previous sections on the calculator.
rate of change = m=
Emphasize the use of appropriate units. For example, in the
, the students see a pool filling at a constant rate of change. Two data points from the
Overview
growth graph or table shown are (4,2) and (6,3). To find the slope, students should calculate:
rate of change = m =
Mention to students that if the graph of a real problem were nonlinear, the calculation of the rate of
change using two data points gives the average rate of change over the interval chosen.
Common Student Errors
Neglecting to write the appropriate units.
Misunderstanding how to use the position with respect to a starting place rather than
distance. In the slope formula, y
Specifying which point is (x
calculations give the same answer. Some students are confused when they see a division by
two negative numbers that results in a positive growth. Discuss this with the students. Watch
for an incorrect substitution where students switch the order in the numerator or
denominator. For example, if the data points (0,0) and (10,2) give the growth of a plant in cm
per day, the rate of change is calculated:
2 N 0
Correct:
10 N 0
0 N 2
Incorrect:
10 N 0
Students need to be exposed to other variables besides x and y. For example, it is useful to
use t for time and d for distance.
Topics in Algebra 1
N y
y
2 1
units
N x
x
2 1
3 N 2
ft 1 ft
= = .5
6 N 4
hr 2 hr
y gives the signed distance traveled.
2 1
,y ) and which point is (x
1 1
0 N 2
cm 1 cm
= or
0 N 10
day 5 day
cm
day
© 2001 Texas Instruments
Section 3: Slope as Rate of Change
Fill the Pool
ft
hr
,y ). Show students that both
2 2
M1
cm cm
=
M5
day day

Teacher Notes

example in the
Teacher Notes 3-24