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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)

101520

$20.00

$45.00$38.75$32.50$26.25

Downloads

answer: 6.25/5 = $1.25/download

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

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:

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

Undefined

What is the slope of the line?

Undefined

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...

EXAMPLE #3:

246810

EXAMPLE #4:

246810

129630

EXAMPLE #5:

-5-3-113

SLOPE from two points...

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

³⁄₅ ½

-¾ ¾

⅔ -¼

x y12345

Review Questions

x y-4-2024

-6-3036

x y-8-5-214

-13-7-1511

1) 2) 3)

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?

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