Chapter 3: Linear Functions Section 2: Slope Using Coordinates
Topics in Algebra 1 © 2001 Texas Instruments Teacher Notes 3-14
Linear Functions: Slope Using Coordinates Teacher Notes
Objectives
•
To introduce slope as a ratio as the change in
y
to the change in
x
.
•
To find the slope of a line using the slope formula.
•
To illustrate the characteristics of lines with positive, zero, negative, or undefined slope.
•
To associate
increasing
,
horizontal
,
decreasing
, or
vertical
with the appropriate slope.
Math Highlights
This section again highlights a review of slope as the steepness of a line. The section opens with
a bike riding along a piecewise linear path. Students see the definition of slope as a ratio.
Slope =
m
=
rise
run
=
change in y
change in x
=
y
2
N
y
1
x
2
N
x
1
Several examples of the calculations are shown. Next, the characteristics of lines with positive,
zero, negative and undefined slopes are summarized.
Common Student Errors
•
Many students are concerned that they have to know which point is (x
1
,
y
1
) and which point
is (x
2
,y
2
). Show that both calculations give the same answer. In the second example below,
some students are confused when they see division with two negative numbers results in a
positive slope. Discuss this. For the line containing the points (0,0) and (10,2), the slope is
calculated by:
2
N
0
10
N
0
=
1
5
or
0
N
2
0
N
10
=
M
1
M
5
=
1
5
•
Watch for an incorrect substitution where students switch the order in the numerator or
denominator. For the example above,
Incorrect:
0
N
2
10
N
0
or
2
N
0
0
N
10
•
This is a good opportunity to open a discussion on different representations of the same
number. Students might write a calculator answer without thinking about whether or not the
representation is the best for the problem. Ask when it is most useful to have the slope
represented in decimal form versus in fraction form.
•
Remind students that they need to use the Order of Operations rules.
•
In the
³
Try-It!
é
section, the correct calculation is (6
−
4)
÷
(2
−
7), not 6
−
4
÷
2
−
7 (where
division would be performed before subtraction).
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