5 1 Rate of Change and Slope Objective

5. 1 Rate of Change and Slope Objective: SWBAT determine the slope of a line given a graph or two ordered pairs.

Mini Quiz 39 1. Find the domain and range of the function: 2. What is the greatest value in the range of y=2 x+4 for the domain {-2, -1, 0, 1}

Quick Preview The diagram at the right shows the side view of a ski lift. 1. What is the vertical change from: a. A to B? 10 feet b. B to C? 40 feet c. C to D? 10 feet 2. What is the horizontal change from: a. A to B? 30 feet 3. Find the ratio of the vertical change to the b. B to C? 30 feet horizontal change for each section of the ski lift. c. C to D 30 feet A 1 B 4 C 1 = ; = B 3 C 3 D 3 4. Which section is the steepest? B to C

Rate of Change What is the rate of change for the data to the left? change of dependent = $15 change 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 Magnum Cedar Point, OH Superman 6 Flags Magic Mountain Ghost Rider Knott’s Berry Farm Xcelerator Knott’s Berry Farm How steep is the steepest roller coaster? Son of Beast King’s Island, OH These are completely 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. 3 Wait for the count of before you say your answer!

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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? m = Slope OR. . . Vertical change Horizontal change Rise m = Slope Run Rise

What sign is it? Show me! Look to see if the slope is increasing Or decreasing

Model # 1: Watch me do the Step 1: three Choose 2 points steps Step 2: Rise = 2 Step 3: Determine the sign itiv e Run = 1 pos Rise Slope = Run Rise 2+ m=2 Run 1

Model # 2: Watch me do the Step 1: Choose 2 points three steps Step 2: Rise Slope = Run = 3 nega tive Step 3: Determine the sign Rise = 1 Rise 1 m = 1/3 Run 3

Practice # 3: Find the slope of this line Run = 2 Rise = 3 Rise Run +

Practice # 4: Find the slope of this line neg ativ e Rise Run = 3 Rise = 1

Slope Formula x 1 y 1 x 2 y 2 5. Given (5, -3) and (-4, 2), find the slope of the line. m=

Slope Formula x 1 y 1 x 2 y 2 6. Given (0, -2) and (4, -2), find the slope of the line. m=

Tell your partner. . . What are the steps to find the slope of a line from a graph? Calculate rise over run. Look at the line to see if the slope is positive or negative.

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?

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?