5.1 Rate of Change and Slope

DO NOW 1.Find the domain and range of the function: 2. What are the range values of y = 2x + 4 for the domain {-2, -1, 0, 1} ?

Aim: What is rate of change/ slope? Do Now: What are the range values for the function y = 2x + 4 if the domain is {-2, -1, 0, 1, 2} ?

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 Ghost Rider Knott’s Berry Farm Xcelerator Knott’s Berry Farm Superman 6 Flags Magic Mountain Son of Beast King’s Island, OH How steep is the steepest roller coaster? 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. Wait for the count of 3 before you say your answer!

negative

positive

zero

undefined

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... Rise Run 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 steps Step 1: Choose 2 points Rise = 2 Run = 1 Rise Run 2 1 m = 2 Step 3: Determine the sign positive Slope = Rise Run Step 2: +

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

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

Practice # 4: Find the slope of this line Rise = 1 Run = 3 Rise Run negative

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.

Slope Formula 5. Given (5, -3) and (-4, 2), find the slope of the line. x1x1 y1y1 x2x2 y2y2 m =

Slope Formula 6. Given (0, -2) and (4, -2), find the slope of the line. x1x1 y1y1 x2x2 y2y2 m =

Wrap Up Rate of Change (includes units) Slope –Positive –Negative –Zero –Undefined 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?