how do you determine the constant of proportionality from a graph?

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)