8-3: slope objectives the student will be able to: find the slope of a line given 2 points and a...
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8-3: SlopeObjectives
The student will be able to:find the slope of a line given 2 points and
a graph.
First by rise/run then using the formula!
Find slope from tables.
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What does the sign mean?
Where would you see this sign?
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What does the 7% mean?
7% is the slope of the road. It means the road drops 7 feet vertically for every 100 feet
horizontally.
7%
So, what is slope???Slope is the steepness of a line.
7 feet
100 feet
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Picking out type of slope.
• Flashcards PDF slides for examples.
• Using the whiteboards, I am going to show you 14 slides. You are to write the type of slope.
+, -, 0 (horizontal), or undefined (vertical)!
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Let’s Review
• Draw the 4 types of slope:
1. 2. 3. 4.
Slope is the STEEPNESS of a LINE!
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Slope can be expressed 4 different ways:
1. A line has a positive slope if it is going uphill from left to right.
2. A line has a negative slope if it isgoing downhill from left to right.
2 1
2 1
( ) vertical change
( ) horizontal change
y y risem
x x run
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3.What is the slope of a horizontal line?
The line doesn’t rise!
m 0
number0
All horizontal lines have a slope of 0.
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4. What is the slope of a vertical line?
The line doesn’t run!
All vertical lines have an undefined slope.
m number
0undefined
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Warm-UP
• Everyone needs 2 colored pencils. For the NCTM activity worksheet “Just Slope”. Please following along.
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Rise/Run
• Pay attention to the next few examples.
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When given the graph, it is easier to apply “rise over run”.
Ex. 1)Determine the slope of the line.
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Start with the lower point and count how much you rise and run to get to the other
point!
Determine the slope of the line.
6
3
run
3
6= =
1
2
rise
Notice the slope is positive AND the line increases!
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Ex. 2) Determine the slope of the line.
The line is decreasing (slope is negative).
2
-1
rise
run
2
1 2
Find points on the graph. Use two of them and apply rise over run.
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Remember…
Slope can be:
• Positive
• Negative
• 0/# = 0
• #/0 = Undefined
• Fractions, improper, 9/7, 11/9, 15/2, etc.
• Decimals ½ = 0.5, ¼ = 0.25, etc.
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Let’s try more
• Using the colored pencils and the NCTM activity triangle worksheet, we will complete more rise/run problems.
• We will do some together then you will complete some on your own.
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Who uses this stuff?
• Let’s think of several jobs that uses angles/slope/rate of change? (look at pdf)
1. roofer
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Recall
1. Horizontal Lines have _________ slope.
2. Vertical Lines have ________ slope.
3. Draw the 4 types of slope AND label the slope
A. B. C. D.
m = m = m = m =
zero
undefined
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Synonyms for slope?
1. angle
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Slope, do we need a formula?
• You may not always be given a graph of the line to determine slope using rise/run. So we need another method.
• Using the slope formula, you can ALWAYS find slope if you know 2 points.
• Remember slope is a rate of change.
Change in y’s/ change in x’s
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1) Find the slope of the line that passes through the points (-2, -2) and (4, 1).
(1 ( 2))
(4 ( 2))m
2 1
2 1
( )
( )
y ym
x x
(1 2)
(4 2)
When given points, it is easier to use the formula!
STEPS for using this formula:
1. LABEL your points- EVERYTIME!!!!!!!!
2. Plug in the formula and simplify the fraction.
13
6 2
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Did you notice that Example #1 and Example #2 were the same problem
written differently?
(-2, -2) and (4, 1)6
31
2slope
You can do the problems either way!Which one do you think is easiest?
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3) Find the slope of the line that goes through the points (-5, 3) and (-2, 1).
m y2 y1
x2 x1
m 1 3
2 ( 5)
m 1 3
2 5
m 2
3
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Graphic Organizer
• Let’s use a graphic organizer to guide us for the method of finding slope using the formula.
• Remember HORIZONTAL lines =
• VERTICAL lines =
zero slope
Undefined slope
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4) Find the slope of the line that passes through (3, 5) and (-1, 4).
Label the points:
A. 4
B. -4
C. ¼
D. - ¼
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5) Determine the slope of the line shown.
A. -2 Could do this 2 ways!!
B. -½
C. ½
D. 2
What would be a real world ex? Think of a pool…
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Practice, Whiteboards1. LABEL 2. plug in 3. simplify
• 1. (1, 1), (3, 4)
• 2. (0, 0), (5, 4)
• 3. (-2, 2), (-1, -2)
• 4. (7, -4), (9, -1)
• 5. (3, 5), (-2, 5)
• 6. (-1, 3), (-1, 0)
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Review
• Handout with slope as a formula (partner slope activity). In partners of 2- here are the groups
• Please complete, check with a neighbor and turn in.
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Collinear Points
• Lie on the same line.
• Points are collinear if they have the same slope.
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Let’s Find Out• Are (3, 5), (4, 7) (7, 13) collinear?
• Calculate the slope the first two points: (3, 5) and (4, 7).
• Calculate the slope for the second pair of points (4, 7) and (7, 13).
• Yes.
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You Try…
• Are (8, 9), (5, 3), and (2, -2) collinear?
• No.
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1
Draw a line through the point (2,0) that has a slope of 3.
1. Graph the ordered pair (2, 0).
2. From (2, 0), apply rise over run (write 3 as a fraction).
3. Plot a point at this location.
4. Draw a straight line through the points.
3
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The slope of a line that goes through the points (r, 6) and (4, 2) is 4. Find r.
To solve this, plug the given information into the formula
m
( y2 y
1)
(x2 x
1)
.
2 64
4 r
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4 4
1 4 r
To solve for r, simplify and write as a proportion.
4 4
1 4 r
2 6
44 r
Cross multiply.
1(-4) = 4(4 – r)
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Simplify and solve the equation.1(-4) = 4(4 – r)
-4 = 16 – 4r-16 -16
-20 = -4r-4 -45 = r
The ordered pairs are (5, 6) and (4, 2)