Math 65. Mod 2. Section 2.1 Rate of Change and Slope of a Line
I. Rate of Change:
A. Linear function:
B. Non­linear function:
Definition: The rate of change
For linear functions: The rate of change is _______________________. II. Slope of a line:
Definition: The slope of a line
III. Finding slope:
A. TABLES: Ex. 1: The table below represents a linear function. Find its slope including units.
h (hours) 1.5 2.0 2,5 3.0 3.5
d (dollars) 11.25 15.00 18.75 22.50 26.25
Choose two points and use the formula. NOTE: Which points don't matter, order of subtraction matters!
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B. GRAPHS:
Ex. 2: Find the slope of the line graphed. M65Sec2.1pg2
Y = ­0.5x + 1
NOTE: Choose two points on the line that are easy to read. (At intersections on the grid.) Also notice that slope is going down from left to right. Pay close attention to scale
Ex. 3: Find the slope of the line graphed. y = 2x ­2
NOTE: Slope is going up from left to right.
C. EQUATIONS: Look at the equations for the two graphs in examples 2 and 3. Notice where slope shows up in each equation.
Definition: The slope of a linear equation
In each of the following, find the slope of the linear equation. NOTE: Solve each for the dependent variable first. Put it into y = ax + b form.
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IV: Three special kinds of straight lines and their equations.
A. Horizontal lines:
Ex. 9: Find the slope of the linear functions below. Determine if it is horizontal.
n
1
­1
­3
­5
­7
p
5
5
5
5
5
x
1
3
5
7
9
z
11
13
15
17
19
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B: Vertical lines: Ex. 10: Find the slopes of each below. Determine if they are horizontal, vertical or neither.
k
­2
­2
­2
­2
­2
m
0
2
4
6
8
p
0
­3
­6
­9
­12
r
­3
­3
­3
­3
­3
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D: Proportions: Ex. 11: Find the rate (slope) of each of the following linear functions. Determine if it is a proportion. If it is, answer the question.
a) Katrina consistently makes 24 out of every 40 baskets she shoots. How many shots will she make if she shoots 75 times?
b) The table below gives times, t, in seconds and distance, d, in inches that an ant can crawl. Find the time it will take for the ant to crawl 1 foot.
t
0
1
2
3
d
0
0.9
1.8
2.7
c) The ice cream at Ice Cream Warehouse as a function of the number of scoops in the bowl. According to this information, how
much will the family sized bowl cost if it contains 12 scoops of ice cream?
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