4.3 Rate of Change and Slope Objective: SWBAT determine the slope of a line given a graph or two ordered pairs.
Transcript
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4.3 Rate of Change and Slope Objective: SWBAT determine the
slope of a line given a graph or two ordered pairs.
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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
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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.
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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 () 198825 199025 199129 200437 200842 What
do you think??? Well lets 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
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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
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The Magnum Cedar Point, OH Ghost Rider Knotts Berry Farm
Xcelerator Knotts Berry Farm Superman 6 Flags Magic Mountain Son of
Beast Kings Island, OH How steep is the steepest roller coaster?
These are completely vertical!
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Imagine a roller coaster moving from LEFT to RIGHT
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There are four different kinds of slope the coaster could
encounter...
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And 2 Special Cases The zero-fun coaster The impossibly scary
coaster What kind of slope are they?
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Aw! Thats zero fun!
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Thats a really scary coaster, so the slope is
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Tell me slope of each line POSITIVE NEGATIVE ZERO POSITIVE
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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
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Start with 2 points on gridline intersections
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How do you calculate the slope of a line? Slope = Vertical
change Horizontal change OR... Rise Run m Slope = m Rise Run
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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:
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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:
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OK, GET READY, AROUND THE ROOM WE GO!!!!!
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Practice # 3: Find the slope of this line Rise Run Rise = 3 Run
= 2
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Practice # 4: Find the slope of this line Rise = -1 Run = 3
Rise Run
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Rise 3 4 Run THE SLOPE IS 3 4
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Find the slope of the following line. The slope is 1 2
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Find the slope of the line. The slope is. -3
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When given the graph, it is easier to apply rise over run. 1)
Determine the slope of the line.
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Determine the slope of the line shown. 1.-2 2.- 3. 4.2
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Determine the slope of the line. The line is decreasing (slope
is negative). -2 1 Find points on the graph. Use two of them and
apply rise over run.
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What is the slope of a horizontal line? The line doesnt rise!
All horizontal lines have a slope of 0.
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What is the slope of a vertical line? The line doesnt run! All
vertical lines have an undefined slope.
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Find the slope of these lines. Black line 3 Red Line 1 Blue
Line-1/2
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Find the slope of these lines Orange line = 0 Green Line =
Undefined
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Determining Slope Rise=1 Slope= 1212 Slope=3 Rise=6 Run =2
Rise=12 Run =4