4.3 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=2x+4 for the domain {-2, -1, 0, 1} Domain: All Real #’s Range: y ≥ -1 y= 2(-2) + 4 =0 y = 2(-1) + 4 = 2 y = 2(0) + 4 = 4 y = 2(1) + 4 = 6 The highest output (y-value) is 6

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 table show the cost of mailing a 1-ounce letter in different years. Find the rate of change in cost for each time interval. During which time interval did the cost increase at the greatest rate? YearCost (¢) What do you think??? Well let’s find the rate of change in each time interval: From 1998 to 1990 From 1990 to 1991 From 1991 to 2004 From 2004 to 2008 = 0 ¢ per year = 4 ¢ per year = 0.62 ¢ per year = 1.25 ¢ per year So the time interval that increased the greatest was from 1990 to 1991

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? 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 A 1 B 4 C 1 B 3 C 3 D 3 = ; = ; = B to C

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…

Tell me slope of each line POSITIVE NEGATIVE ZERO POSITIVE

How do you calculate the slope of a line? 1.Pick two points on the line 2.Calculate “rise over run”

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

Model # 1: Watch me do the three steps Step 1: Choose 2 points Rise = 2 Run = 1 Rise Run 2 1 m = 2 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 Slope = Rise Run Step 2:

OK, GET READY, AROUND THE ROOM WE GO!!!!!

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

Rise 3 4 Run THE SLOPE IS 3 4

Find the slope of the following line. The slope is… 1 2

Find the slope of the line. The slope is…. -3

When given the graph, it is easier to apply “rise over run”. 1) Determine the slope of the line.

Determine the slope of the line shown ½ 3.½ 4.2

Determine the slope of the line. The line is decreasing (slope is negative) Find points on the graph. Use two of them and apply rise over run.

What is the slope of a horizontal line? The line doesn’t rise! All horizontal lines have a slope of 0.

What is the slope of a vertical line? The line doesn’t run! All vertical lines have an undefined slope.

Find the slope of these lines. Black line 3 Red Line 1 Blue Line-1/2

Find the slope of these lines Orange line = 0 Green Line = Undefined

Determining Slope Rise=1 Slope= 1212 Slope=3 Rise=6 Run =2 Rise=12 Run =4