4.3 4.4 notes a
TRANSCRIPT
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Write 1 pair of points or slopes for each of the following statements:
a. a positive slope and a negative slope that is steeper
b. a negative slope and a positive slope with the same steepness
c. two pairs of points that have the same slope
d. a pair of points whose slope is undefined
e. a pair of points whose slope is zero
Opener:
Complete these questions in your notes with your partner.
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Homework Questions:
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January 6th & 7th: 4.3 Rates of Change
Launch:
How does the pace of 8 mph that you calculated in exercise 10 relate to this graph?
Speed the rate at which the location of an object changes
average speed = distance time
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Finding the average speed between points
What is Tia's average speed between the following points?
a. O and A
b. A and B
c. B and C
d. O and C
When was Tia traveling the fastest?
Would you have been able to tell this even without the specific units labeled? How so?
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Slope and Average Speed
The slope between two points on a distance‐time graph is the ___________ ________ of travel between those two points.
Partner A: Explain this theorem to your partner in your own words.Partner B: Listen carefully to see if there's anything you think that needs to be added in.
Distance‐Time Graphs
In which graph are you moving steadily? Speeding up gradually? Slowing down gradually? Explain.
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Speed ‐ Time Graphs In which graph are you moving steadily? Speeding up gradually ? Slowing down gradually? Explain.
Distance-Time Graphs vs. Speed-Time Graphs
Distance‐Time: speed is change of distance over ________ interval of time
Speed‐Time: speed is change of distance over ________ interval of time
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Slope = Rate of Change
What are some other examples of rate of change problems we can find comparing two quantities?
Checkpoint!Open your books to page 324.
5a.) How many miles was Ryota’s trip? How long did it take, including the alleged nap?
5b.) Sketch two possible distance‐time graphs for Ryota’s trip. Include his nap in one graph but not in the other.
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4.4 Collinearity
Launch:Pg. 331
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Collinear Points Points that all lie on the same line.•
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Pg. 328
How can you tell if three points lie on a horizontal line?
On a vertical line?
On any line?
Determining Collinearity
What are some possible ways to determine whether three points are collinear by looking at their coordinates?
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Using Slope to Determine Collinearity
Points A, B, and C are collinear if...
Checkpoint! Complete # 2‐5 under "For You to Do" on page 329. Be prepared to share your answers with the rest of the class. (7 minutes)
Are the three points collinear?A (‐1,3), B (4, 15), C (14, 39)
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Homework: SAME as assignment sheet for today :
Pg. 325, Pg. 330, & graphing review
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