How do you determine the constant of proportionality from a graph?
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Transcript of How do you determine the constant of proportionality from a graph?
![Page 1: How do you determine the constant of proportionality from a graph?](https://reader036.fdocuments.in/reader036/viewer/2022081501/56812cec550346895d91b1a4/html5/thumbnails/1.jpg)
How do you determine the constant of proportionality from a graph?
0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
50
100
150
200
Hours
Miles
(0,0)(1,45)
(2,90)
(3,135)
(4,180)
![Page 2: How do you determine the constant of proportionality from a graph?](https://reader036.fdocuments.in/reader036/viewer/2022081501/56812cec550346895d91b1a4/html5/thumbnails/2.jpg)
In this lesson you will learn how to determine the constant of proportionality in graphs by
finding the ratio of y to x.
![Page 3: How do you determine the constant of proportionality from a graph?](https://reader036.fdocuments.in/reader036/viewer/2022081501/56812cec550346895d91b1a4/html5/thumbnails/3.jpg)
Let’s Review
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
-6
-4
-2
0
2
4
6
(2,5)
(2,-5)
(-2,5)
(-2,-5)
y
x
![Page 4: How do you determine the constant of proportionality from a graph?](https://reader036.fdocuments.in/reader036/viewer/2022081501/56812cec550346895d91b1a4/html5/thumbnails/4.jpg)
A Common Mistake
Graph of a Proportional Relationship:
![Page 5: How do you determine the constant of proportionality from a graph?](https://reader036.fdocuments.in/reader036/viewer/2022081501/56812cec550346895d91b1a4/html5/thumbnails/5.jpg)
Core Lesson
What is the constant of proportionality?
0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
50
100
150
200
Hours
Miles
(0,0)(1,45)
(2,90)
(3,135)
(4,180)
![Page 6: How do you determine the constant of proportionality from a graph?](https://reader036.fdocuments.in/reader036/viewer/2022081501/56812cec550346895d91b1a4/html5/thumbnails/6.jpg)
Core Lesson
y = kx
Let x and y be two proportional quantities.Let k be a constant.
y
x= k x
y= 1
k
![Page 7: How do you determine the constant of proportionality from a graph?](https://reader036.fdocuments.in/reader036/viewer/2022081501/56812cec550346895d91b1a4/html5/thumbnails/7.jpg)
Core Lesson
y = kx
y = distance (miles)k = unit rate of miles per hour (speed)
x = time (hours)
y
x= k x
y= 1
k
![Page 8: How do you determine the constant of proportionality from a graph?](https://reader036.fdocuments.in/reader036/viewer/2022081501/56812cec550346895d91b1a4/html5/thumbnails/8.jpg)
Core Lesson
0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
50
100
150
200
Hours
Miles
(0,0)(1,45)
(2,90)
(3,135)
(4,180)
45
1
90
2
1353
1804
y
x
![Page 9: How do you determine the constant of proportionality from a graph?](https://reader036.fdocuments.in/reader036/viewer/2022081501/56812cec550346895d91b1a4/html5/thumbnails/9.jpg)
Core Lesson
45
1= 45 90
2= 45
1353
= 45 1804
= 45
![Page 10: How do you determine the constant of proportionality from a graph?](https://reader036.fdocuments.in/reader036/viewer/2022081501/56812cec550346895d91b1a4/html5/thumbnails/10.jpg)
Core Lesson
y = distance (miles)k = miles per hour (speed)
x = time (hours)
k = 45 miles per houry = 45 x
![Page 11: How do you determine the constant of proportionality from a graph?](https://reader036.fdocuments.in/reader036/viewer/2022081501/56812cec550346895d91b1a4/html5/thumbnails/11.jpg)
In this lesson you have learned how to determine the constant of proportionality in graphs by
finding the ratio of y to x.
![Page 12: How do you determine the constant of proportionality from a graph?](https://reader036.fdocuments.in/reader036/viewer/2022081501/56812cec550346895d91b1a4/html5/thumbnails/12.jpg)
Guided Practice
What is the constant of proportionality?
0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
50
100
150
Hours
Miles
(1,30)
(2,60)
(3,90)(4,120)
![Page 13: How do you determine the constant of proportionality from a graph?](https://reader036.fdocuments.in/reader036/viewer/2022081501/56812cec550346895d91b1a4/html5/thumbnails/13.jpg)
Extension Activities
Barbara’s beagle needs to be walked each morning and evening. Barbara and the dog usually walk for 20 minutes and travel 3/5 of a mile each morning and evening. Graph the relationship between distance and time in this problem. How many miles will Barbara travel in 7 days? How much time will she spend walking?
![Page 14: How do you determine the constant of proportionality from a graph?](https://reader036.fdocuments.in/reader036/viewer/2022081501/56812cec550346895d91b1a4/html5/thumbnails/14.jpg)
Extension Activities
To return home, Jason left the Wellington, New Zealand hotel at 4 AM and arrived at his home airport in Albany, New York at 11:30 PM Eastern Standard Time (EST) on the same day of the week. He traveled west to east. How long did it take him to make the trip? Hint: Thursday at 7 PM EST is noon on Friday in Wellington.
![Page 15: How do you determine the constant of proportionality from a graph?](https://reader036.fdocuments.in/reader036/viewer/2022081501/56812cec550346895d91b1a4/html5/thumbnails/15.jpg)
Extension Activities
Ashley ran 100 yards in 12 seconds. What was her speed in miles per hour? Round your answer to the nearest hundredth.
![Page 16: How do you determine the constant of proportionality from a graph?](https://reader036.fdocuments.in/reader036/viewer/2022081501/56812cec550346895d91b1a4/html5/thumbnails/16.jpg)
Quick Quiz
What is the constant of proportionality?
0 0.5 1 1.5 2 2.5 3 3.5 4 4.50
50100150200250
Hours
Miles
(1,50)(2,100)
(3,150)(4,200)