Slope of a Line Thinker See if you can tell me the four types of slope and draw them!
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Transcript of Slope of a Line Thinker See if you can tell me the four types of slope and draw them!
Slope of a LineThinker
See if you can tell me the four types of slope and draw them!
Types of Slope
PositiveNegative
Zero
Undefinedor
No Slope
Common Core Objective # 30•Finding the AOC or SLOPE on a table or
graph.
Slope is the measure of the steepness of a line.
•
The letter “m” isused to represent
slope.
Why? Why not?
Slope of a line is its rate of change. Often the letter m is used. Change is often symbolized in mathematics by a delta for which the symbol is the Greek letter: Δ
If given 2 points on a line, you may findthe slope using theformula m = y2 – y1
x2 – x1
Find the slope of the line through the
points (3,7) and (5, 19).x1 y1 x2 y2
m = 19 – 7 5 – 3
m = 12 2 m = 6
(3, 4) and (-6, -2)m = -2 – 4 -6 – 3
m = -6 -9
m = ⅔
USING A TABLE
• How would one find the slope of this table?
• Find the change in y-values compared to the change in x-values.
• It has an AOC or SLOPE of 2
USING A TABLE
• Find the slope of this table.• It does not have one constant rate of
change but each interval has it’s on.• What could one have done to verify?• GRAPHING IS A POSSIBILITY
Another method to use when given a graph
Is RISE RUN
rise = 4
run = 5
m= rise runm= 4/5
SPECIAL CASES OF SLOPE
• HOW DO YOU GET ZERO OR UNDEFINED FROM A SET OF POINTS?
2 special cases of slopeGiven the points (5,4)
and (1,4), if you use the slope formula you will come out with
m = 0 -4 Or just 0 since it is the
numerator and 0 divided by –4 is ALWAYS 0
Given the points (4,2) and (4,9), if you use the slope formula you will come out with
m = 7 0However, 0 in the However, 0 in the
denominator denominator IS IS NOT 0 but NOT 0 but UNDEFINED!UNDEFINED!
Special Case SamplesM=0 M=Undefined
• 1.
Notebook Examples• Find the slope of the
line given two points or a graph:
• (1) (1, 2), (4, 8)• (2) (-5, 2), (1, -4)• (3) (7, 6), (3, 6)• (4) (2, 6), (8, 1)
•
• Answers• (1) m = 2• (2) m = -1• (3) m = 0• (4) m = -5/6• (5) Undefined• (6) m = -3/2
(6)
(5)
HOMEWORK• You will have a 10 question quiz –
1 point each Monday about the following three topics.
• (1) Slope-Intercept Form• (2) Standard Form of a line• (3) Point-Slope Form• Each has an equation and is used
for different purposes• You can use your notes