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...


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


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


A company is launching a new product. The graph below represents the relationship between units sold and earnings.


Rate of change: $100/unit


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.


Rate of change: $100/unit


Rate of Change from a Graph...



.50 cents/download






Rate of Change from a Table...


EXAMPLE #1:The table shows the relationship between

the number of minutes and the cost of a phone call.


answer: .75/15 = 5 cents/min


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


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.



DOMINO EFFECT







Types of Slope


Types of Slope

positiv

e slop

e negative slopezero slope

undefined slope


Types of Slope

positiv

e slop

e negative slopezero slope

undefined slope

?



SLOPE from a Graph...


Slope is measured as:

Rise

Run

Vertical Change

Horizontal Change

Change in y

Change in x= =


SLOPE= rise run


SLOPE= rise run Think:

"rise" down -> negative"run" left -> negative


SLOPE= rise run


SLOPE= rise run Note:

"m" is the variable we always use for slope


SLOPE= rise run


SLOPE= rise run

Undefined


What is the slope of the line?



Undefined






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 from a Table...


#1)


#2)


x y

EXAMPLE #3:

12345

246810


x y

EXAMPLE #4:

246810

129630


x y

EXAMPLE #5:

-5-3-113

54321


SLOPE from two points...


#1)


#2)


Find the slope of the line that passes through the points

(4, 5) and (2, 3)

EXAMPLE #3:



(-3, -5) and (-2, 3)

EXAMPLE #4:



(-1, 5) and (7, 5)

EXAMPLE #5:


Problem of the Day


REVIEW:


SLOPE - measures the steepness (rate of change) of a line.


change in ychange in xSLOPE rise

run∆ y∆ x= ==


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


Circle the steeper slope

-5 ½

4 -3

³⁄₅ ½

-¾ ¾

⅔ -¼


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)

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