5.1 Rate of Change and Slope

5.1 Rate of Change and SlopeObjective: SWBAT determine the slope of a line given a graph or two ordered pairs.Mini Quiz 39Find 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}

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The diagram at the right shows the side view of a ski lift.What is the vertical change from: A to B?B to C?C to D?What is the horizontal change from:A to B?B to C?C to DFind the ratio of the vertical change to the horizontal change for each section of the ski lift.

Which section is the steepest?10 feet40 feet10 feet30 feet30 feet30 feetA 1 B 4 C 1B 3 C 3 D 3= ; = ; =B to CRate of 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 RiderKnotts Berry Farm

XceleratorKnotts Berry Farm

Superman6 Flags Magic Mountain

Son of BeastKings Island, OHHow steep is the steepest roller coaster?These arecompletelyvertical!Imagine a roller coaster moving from LEFT to RIGHT

There are four different kinds of slope the coaster could encounter...

UphillPositiveSlope

DownhillNegativeSlopeAnd 2 Special Cases

The zero-fun coasterThe impossibly scary coasterWhat kind of slope are they?HorizontalZeroSlope

Aw!Thats zero fun!Vertical

UndefinedSlopeThats a really scary coaster, so the slope isFor 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!123negative

123positive

123zero

123undefined

How do you calculate the slope of a line?Pick two points on the lineCalculate rise over runDetermine the signThere are 3 steps:Start with 2 points on gridline intersections OKOKOKOKNot OKNot OKNot OKOKOKOKOKStep 1(-1, -3)(0, -1)(1, 1)(2, 3)How do you calculate the slope of a line?Slope =Vertical changeHorizontal changeOR...RiseRundivided bydivided bymSlope =mStep 2RiseRun What sign is it?Step 3Look to see if the slope is increasingPositiveOr decreasingNegative

Show me!Model # 1: Watch me do the three stepsStep 1: Choose 2 points Rise = 2Run = 1RiseRundivided by21m = 2Step 3:Determine the signpositiveSlope =RiseRundivided byStep 2:

+Model # 2: Watch me do the three stepsStep 1: Choose 2 points Rise = 1Run = 3RiseRundivided by13m = 1/3Step 3:Determine the signnegativeSlope =RiseRundivided byStep 2:

-Practice # 3: Find the slope of this lineRiseRundivided byRise = 3Run = 2

Think Pair Share

+Step 1: Choose Two pointsStep 2: Rise Over RunStep 3: Determine SignPractice # 4: Find the slope of this line Think Pair ShareStep 1: Choose Two pointsStep 2: Rise Over RunStep 3: Determine SignRise = 1Run = 3

RiseRundivided by

negativeSlope Formula

5. Given (5, -3) and (-4, 2), find the slope of the line.x1y1x2y2m =

Slope Formula

6. Given (0, -2) and (4, -2), find the slope of the line.x1y1x2y2m =

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 UpRate of Change (includes units)Slope

PositiveNegativeZeroUndefinedHW: P. 234 #1-29 odd, 75-85 oddDLUQ: Whats the difference between slope and rate of change?

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?