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Determine Rate of Change
Examples: Notes:
Rise: Vertical Change (y)
Run: Horizontal Change (x)
Rise over Run (of a step): the vertical and the horizontal changes in a graph between 2 points on the line.• Representation of the rate of change shown
in a graph
slope
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2.2 Characteristics of Graphs
#
Examples: Notes:
Rate: a ratio in which the 2 quantities being compared are measured in different units.• Written in fractional form • Always labeled
Rate of Change: used to describe the rate of increase or decrease.
Per: for each or for every
Unit Rate: a comparison of 2 meausrements in which the denominator has a vale of 1• Written in fractional form • Always labeled
Unit Rate of Change: once the fraction is reduced/divided out to have 1 as its denominator.
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Finding Slope of a Line
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Examples: Notes:
Finding the steepness of stairs = same as finding the steepness of a line.
Slope = rate of change = steepness of a line• Fraction of the change in rise (y) over run (x)• Represented by letter "m"
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Finding Slope of a Line
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Examples: Notes:
Positive Slopes: RISES from left to right.• m > 0
Negative Slopes: FALLS from left to right.• m < 0
Horizontal Slopes: ZERO slope• y = 3• Where line crosses the y-axis
Vertical Slopes: UNDEFINED• If a step doesn't go up, then it's not a step!• You can't divide by zero• m = undefined
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Horizontalero
VerticalPositive Negativeundefined
Slope of a Line
increases decreases
NOTES
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Finding Slope of a Line
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Examples: Notes:
How to find the slope of a graph:1. Find 2 clear points on line2. Starting on the farthest left point, count
how many units up or down until you are in line with the next point = NUMERATOR
> Positive (+) if it moves up> Negative (-) if it moves down
3. Count how many units over to the right until you hit the next point = DENOMINATOR.
A slope of 4/3 means down 4 over 3 from
point to point
13
slope =
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m =
Find the Slope
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-15
-2
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Finding Slope of a Line4/5/18 #
Examples: Notes:
Finding Slope from formula1. Assign the first point as
and the second point as2. Use slope formula
3. Plug values in & simplify:
Find the slope of a line passing through points (-2, 4) and (3, 6)
Point Slope Formula
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Assignment Answers
1/22
-3/2 -1/2 -3
-2/3 7/4 -5/6
1 2
-3/2y = 4
-3/41
-20
100-600-2
40-2=
166-14856-42
1814= 9
7=
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Finding Slope of a Line12/14/18 #
Examples: Notes:
Find slope from Table: Rage of Change1. Select any 2 points from a table
> (0, 6) and (4, 9)
2. Identify points as 3. Use Point Slope Formula to find slope.
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Finding Slope of a Line4/5/18 #
Examples: Notes:To graph a line given a point and the Slope:1. Plot the single point that is provided.2. From that point, count how many units up
or down the numerator of the slope is. > If slope is positive, move up.> If the slope is negative, move down.
3. Then, count how many units over to the right from the denominator of the slope.
4. Plot a new point there, repeat to plot another point and connect the points to draw a straight line.
m = ½
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