Warm-upgcmath.weebly.com/uploads/2/1/1/5/21159736/slope.pdf · WARM-UP #2 Change in the DEPENDENT...
Transcript of Warm-upgcmath.weebly.com/uploads/2/1/1/5/21159736/slope.pdf · WARM-UP #2 Change in the DEPENDENT...
SLOPE! October 27, 2014
Warm-up...
SLOPE! October 27, 2014
Lucy has already sold 154 boxes of Girl Scout cookies. She sells the same amount of boxes each day. After 10 more days, Lucy has sold a total of 374 boxes of Girl Scout cookies.
At what rate does Lucy sell boxes of cookies?
WARM-UP #1
Change in the DEPENDENT variable: 374-154 = 220
Change in the INDEPENDENT variable: 10 - 0 = 10
Rate of Change: 220/10 = 22 boxes/day
SLOPE! October 27, 2014
A company is launching a new product. After selling 20 units, the company made $32,000 of earnings. After selling 40 units, the company
made $34,000 in earnings.
What is the rate of change?
WARM-UP #2
Change in the DEPENDENT variable: 34,000 - 32,000 = 2,000
Change in the INDEPENDENT variable: 40 - 20 = 20
Rate of Change: 2,000/20 = $100/unit
SLOPE! October 27, 2014
A company is launching a new product. The graph below represents the relationship between units sold and earnings.
What is the rate of change?
Rate of change: $100/unit
SLOPE! October 27, 2014
Units Sold Earnings
0 30,000
10 31,000
20 32,000
30 33,000
40 34,000
50 35,000
A company is launching a new product. The table below represents the relationship between units sold and earnings.
What is the rate of change?
Rate of change: $100/unit
SLOPE! October 27, 2014
Rate of Change from a Graph...
SLOPE! October 27, 2014
What is the rate of change?
.50 cents/download
SLOPE! October 27, 2014
What is the rate of change?
SLOPE! October 27, 2014
What is the rate of change?
SLOPE! October 27, 2014
Rate of Change from a Table...
SLOPE! October 27, 2014
EXAMPLE #1:The table shows the relationship between
the number of minutes and the cost of a phone call.
What is the rate of change?
answer: .75/15 = 5 cents/min
SLOPE! October 27, 2014
EXAMPLE #2:The table shows the relationship between
the number of music downloads and the cost.What is the rate of change?
Cost(in dollars)
05
101520
$20.00
$45.00$38.75$32.50$26.25
Downloads
answer: 6.25/5 = $1.25/download
SLOPE! October 27, 2014
SLOPE
SLOPE! October 27, 2014
SLOPE - a function's rate of change. (Lines have a constant rate of change.)
Slope measures how steep a line is.
The greater the rate of change, the steeper it will be.
SLOPE! October 27, 2014
SLOPE! October 27, 2014
DOMINO EFFECT
SLOPE! October 27, 2014
SLOPE! October 27, 2014
SLOPE! October 27, 2014
SLOPE! October 27, 2014
SLOPE! October 27, 2014
SLOPE! October 27, 2014
Types of Slope
SLOPE! October 27, 2014
Types of Slope
positiv
e slop
e negative slopezero slope
undefined slope
SLOPE! October 27, 2014
Types of Slope
positiv
e slop
e negative slopezero slope
undefined slope
?
SLOPE! October 27, 2014
SLOPE! October 27, 2014
SLOPE from a Graph...
SLOPE! October 27, 2014
Slope is measured as:
Rise
Run
Vertical Change
Horizontal Change
Change in y
Change in x= =
SLOPE! October 27, 2014
SLOPE= rise run
SLOPE! October 27, 2014
SLOPE= rise run Think:
"rise" down -> negative"run" left -> negative
SLOPE! October 27, 2014
SLOPE= rise run
SLOPE! October 27, 2014
SLOPE= rise run Note:
"m" is the variable we always use for slope
SLOPE! October 27, 2014
SLOPE= rise run
SLOPE! October 27, 2014
SLOPE= rise run
Undefined
SLOPE! October 27, 2014
What is the slope of the line?
SLOPE! October 27, 2014
What is the slope of the line?
Undefined
SLOPE! October 27, 2014
What is the slope of the line?
SLOPE! October 27, 2014
What is the slope of the line?
SLOPE! October 27, 2014
C
BA
Josh says that the slope from points B to C is steeper than the slope from points A to B.
Do you agree or disagree? Explain your opinion.
the slope is always two because lines have a constant rate of change
SLOPE! October 27, 2014
SLOPE from a Table...
SLOPE! October 27, 2014
#1)
SLOPE! October 27, 2014
#2)
SLOPE! October 27, 2014
x y
EXAMPLE #3:
12345
246810
SLOPE! October 27, 2014
x y
EXAMPLE #4:
246810
129630
SLOPE! October 27, 2014
x y
EXAMPLE #5:
-5-3-113
54321
SLOPE! October 27, 2014
SLOPE from two points...
SLOPE! October 27, 2014
#1)
SLOPE! October 27, 2014
#2)
SLOPE! October 27, 2014
Find the slope of the line that passes through the points
(4, 5) and (2, 3)
EXAMPLE #3:
SLOPE! October 27, 2014
Find the slope of the line that passes through the points
(-3, -5) and (-2, 3)
EXAMPLE #4:
SLOPE! October 27, 2014
Find the slope of the line that passes through the points
(-1, 5) and (7, 5)
EXAMPLE #5:
SLOPE! October 27, 2014
Problem of the Day
SLOPE! October 27, 2014
REVIEW:
SLOPE! October 27, 2014
SLOPE - measures the steepness (rate of change) of a line.
SLOPE! October 27, 2014
change in ychange in xSLOPE rise
run∆ y∆ x= ==
SLOPE! October 27, 2014
The sign of the slope determines the direction.
The value of the slope tells you how steep the line is.Greater slope = steeper line
positiv
e slop
e negative slope
-½ -3
Greater rate of change = steeper line
SLOPE! October 27, 2014
Circle the steeper slope
-5 ½
4 -3
³⁄₅ ½
-¾ ¾
⅔ -¼
SLOPE! October 27, 2014
x y12345
048
1216
Review Questions
x y-4-2024
-6-3036
x y-8-5-214
-13-7-1511
Name
1) 2) 3)
4) 5)
The line that passes through the points
(2, 6) and (4,5)
The line that passes through the points
(-8, 3) and (-4, 6)
DIRECTIONS: Find the slope of each line.
Which line(s) has the steepest slope in questions 1-8?
6)
7) 8)
9)