ALGEBRA Unit Plan – Properties of Linear Functions (Rate of Change/Slope)
Vocabulary
Constant
EXAMPLE:
rate of change
EXAMPLE:
Domain
EXAMPLE:
Range
EXAMPLE:
independent variable
EXAMPLE:
dependent variable
EXAMPLE:
Function
EXAMPLE:
Rule
EXAMPLE:
Table
EXAMPLE:
Linear function
EXAMPLE:
Linear equation
EXAMPLE:
rate of change
EXAMPLE:
Slope
EXAMPLE:
Rise
EXAMPLE:
Run
EXAMPLE:
Delta y
EXAMPLE:
Delta x
EXAMPLE:
OBJECTIVES
(3) Linear functions, equations, and inequalities. The student applies the mathematical process
standards when using graphs of linear functions, key features, and related transformations to
represent in multiple ways and solve, with and without technology, equations, inequalities, and
systems of equations. The student is expected to:
(A) determine the slope of a line given a table of values, a graph, two points on the line, and
an equation written in various forms, including y = mx + b, Ax + By = C, and y - y1 = m(x x1);
(B) calculate the rate of change of a linear function represented tabular, graphically, or
algebraically in context of mathematical and real-world problems;
(C) graph linear functions on the coordinate plane and identify key features, including xintercept, y-intercept, zeros, and slope, in mathematical and real-world problems;
(E) determine the effects on the graph of the parent function f(x) = x when f(x) is replaced
by af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d
Essential Questions:
How can the slope of a linear function be represented in many ways?
What are real world examples of rates of change?
What does it mean for a line to have a positive, negative, zero, or undefined
slope?
PRE-ASSESSMENT
PRE-ASSESSMENT
Pre-requisite skills:
The previous Unit over Linear Patterns should be passed with at least an 80% to be successful on this unit.
SCORE:_______/100
Review for Slope Test
Determine if the relationships in the tables are linear.
1.
2.
3.
x
y
x
y
0
10
0
6
1
8.5
3
8
2
7
6
12
3
5.5
9
18
x
y
1
1
3
7
7
19
10
28
Video: Slope
Is it Linear? Circle Yes or No
Is it Linear? Circle Yes or No
Is it Linear? Circle Yes or No
If yes,
If yes,
If yes,
m = _______
m = _______
m = _______
The following tables are linear. Write the slope.
4.
x
y
6
21
8
29
10
37
12
45
5.
x
4
5
6
7
y
-2
-3
-4
-5
m = _______
m = ________
6. For each of the following, write LINEAR or NOT LINEAR to describe each function.
a)
y  4  6x
______________
b)
y  2x 2
________________
c)
y  6
1
x
2
d)
________________
y
5
x
_______________
Find the slope of the line passing through the two points.
7. (12, 11) and (15, 3)
10. (3,2) and (– 1, 22)
8. (-3, 13) and (-5, -7)
11. (– 6, 4) and ( 2, 4)
9. (9,-6) and (-8, -6)
12. (3, 6) and (3, – 9)
Choose any two points to count the slope of the lines. Circle the slope below.
13.
14.
Circle the correct slope
-3/4
3/4
4/3
-4/3
15.
Circle the correct slope
-5/1
-1/5
5/1
Circle the correct slope
1/5
0 7 undefined/no slope 1
16. What is the slope of the line shown on each graph?
a)
b)
m = _______________
m = _______________
17. For each of the following, write the slope of the equation.
3
y   x6
a)
5
m = _______
b)
5  2x  y
m = _______
c)
y 8
m = _______
d)
y  5x  7
m = _______
18. A plane at an altitude of 33,000 feet begins it’s descent for landing. It descends 100 feet every 10 minutes until it is
on the ground. The elevation, y, is a linear function of the number of minutes, x the plane is decending. What does the
slope of the function represent?
19. Sara is planning a trip to California in the Spring. The round-trip plane ticket is $450 and the hotel costs $135 per
night. The total cost of the trip can be expressed as a linear function, depending on the number of nights she stays. What
is the slope of the graph of this linear function?
Word problem for # 20-22: Mike is mowing lawns for a summer job. He charges a different amount depending on the
time it takes him to mow the lawn. He also charges a fixed rate for the gasoline he uses to mow the lawn.
20. Complete the process column.
# of hours
Mike’s earnings
2
$12.00
3
$16.50
4
$21.00
21. What does the ordered pair (3, $16.50) mean in the table above?
22. What is the rate of change of the table above? _________ Describe what the rate of change means in Mike’s scenario.
23. If y= 15.95x + 24 is a function relating the cost, y, of buying x amount
of student concert tickets, what do you think the slope represents?
___________________________________________
What number is the slope? __________
Write the slope on the grid on the right and bubble in the answer.
24.
a) What is the rate of change?
_____________________
b) In words, what does the rate of change represent?