3-4 Rate of Change and Slope

Objective: SWBAT determine the slope of a line given a

graph or two ordered pairs.

Mini Quiz 391. Find the domain and range of the function:

2. What is the greatest value in the range of y=2x+4 for the domain {-2, -1, 0, 1}

Quick PreviewThe diagram at the right shows the

side view of a ski lift.

1. What is the vertical change from:

a. A to B?

b. B to C?

c. C to D?

2. What is the horizontal change from:

a. A to B?

b. B to C?

c. C to D

3. Find the ratio of the vertical change to the horizontal change for each section of the ski lift.

4. Which section is the steepest?

10 feet

40 feet

10 feet

30 feet

30 feet

30 feet A 1 B 4 C 1B 3 C 3 D 3

= ; = ; =

B to C

Rate of Change

change of Rate variabledependent in the change

t variableindependen in the change

What is the rate of change for the data to the left?

change of dependent = $15change of independent = 1 day

$15 = $15/day 1 day

What does the rate of change mean?It cost $15 more to rent a computer each day.

The MagnumCedar Point, OH

Ghost RiderKnott’s Berry

FarmXcelerator

Knott’s Berry Farm

Superman6 Flags Magic

Mountain

Son of BeastKing’s Island, OH

How steep is the steepest roller coaster?

These arecompletely

vertical!

Imagine a roller coaster moving from LEFT to RIGHT

There are four different kinds of slope the coaster

could encounter...

And 2 Special Cases…

The zero-fun coaster

The impossibly

scary coaster

What kind of slope are

they?

Aw!That’s zero fun!

That’s a really scary coaster, so the slope

is…

For the following slides,call out whether the slope is positive, negative, zero,

or undefined.

Wait for the count of 3 before you say your

answer!

negative

posit

ive

zero

und

efined

How do you calculate the slope of a line?

1. Pick two points on the line

2. Calculate “rise over run”3. Determine the sign

Start with 2 points on gridline intersections

How do you calculate the slope of a line?

Slope =

Vertical change

Horizontal change

OR... RiseRun

m

Slope =m

Rise

Run

What sign is it?

Look to see if the slope is increasing

Or decreasing

Show me!

Model # 1: Watch me do the three stepsStep 1: Choose 2 points

Rise = 2

Run = 1

RiseRun21

m = 2

Step 3:Determine

the sign

posi

tive

Slope =

RiseRun

Step 2:

+

Model # 2: Watch me do the three stepsStep 1: Choose 2 points

Rise = 1

Run = 3

RiseRun13

m = 1/3

Step 3:Determine

the sign

negative

Slope =

RiseRun

Step 2:

-

Practice # 3: Find the slope of this line

RiseRun

Rise = 3

Run = 2

23

m+

Practice # 4: Find the slope of this line

Rise = 1

Run = 3

31

m

RiseRun

negative

Slope Formula

12

12

xx

yym

5. Given (5, -3) and (-4, 2), find the slope of the line.

x1 y1 x2 y2

m =54

)3(2

9

5

Slope Formula

12

12

xx

yym

6. Given (0, -2) and (4, -2), find the slope of the line.

x1 y1 x2 y2

m =04

)2(2

4

0 0

Tell your partner...What are the steps to find the slope

of a line from a graph?

Calculaterise over run.

Look at theline to see ifthe slope is positive ornegative.

Wrap Up• Rate of Change (includes units)• Slope

– Positive– Negative– Zero– Undefined

HW: P. 234 #1-29 odd, 75-85 odd

DLUQ: What’s the difference between slope and rate of change?

run

rise

12

12

xx

yym

Before you leave:

1. What type of slope is shown? (Positive, negative, zero or undefined?)

2. What would a slope of -1/2 look like? (Uphill, downhill, steep, shallow)

3. What is the slope of the line above?