how do you determine the constant of proportionality from a graph?
DESCRIPTION
How do you determine the constant of proportionality from a graph?. (4,180). (3,135). (2,90). (1,45). ( 0 ,0). In this lesson you will learn how to determine the constant of proportionality in graphs by finding the ratio of y to x. y. (-2, 5). (2,5). x. (-2,-5). (2, -5). - PowerPoint PPT PresentationTRANSCRIPT
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)
In this lesson you will learn how to determine the constant of proportionality in graphs by
finding the ratio of y to x.
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
A Common Mistake
Graph of a Proportional Relationship:
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)
Core Lesson
y = kx
Let x and y be two proportional quantities.Let k be a constant.
y
x= k x
y= 1
k
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
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
Core Lesson
45
1= 45 90
2= 45
1353
= 45 1804
= 45
Core Lesson
y = distance (miles)k = miles per hour (speed)
x = time (hours)
k = 45 miles per houry = 45 x
In this lesson you have learned how to determine the constant of proportionality in graphs by
finding the ratio of y to x.
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)
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?
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.
Extension Activities
Ashley ran 100 yards in 12 seconds. What was her speed in miles per hour? Round your answer to the nearest hundredth.
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)