how can you use a graph to determine whether two rates are the same? for example: on saturday, jen...
TRANSCRIPT
How can you use a graph to determine whether two rates are the same?
For example:On Saturday, Jen walked 2.4 miles in 45
minutes. On Sunday, Jen walked 3.2 miles in 60 minutes. Did Jen walk at
the same rate on Saturday and Sunday?
In this lesson you will learn how to determine if two rates are equivalent by graphing.
Let’s Review
oranges total fruit
= oranges:total fruit
applesoranges
= apples:oranges
Ratios
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
(x,y)
Up or down?Left or right?
Positive xNegative x
Positive y
Negative y
Core Lesson
Graphing Jen’s Walking Rate:
Let x = time spent walking
Let y = distance walked
Core Lesson
Time(mins.)
Distance(miles)
45
60
2.4
3.2 Dis
tance
(m
iles)
Time (mins.)
Jen’s Walking Rate
6543210
0 15 30 45 60
(45,2.4)
(60,3.2)
Core Lesson
Time(hours)
Distance(miles)
0.75
1
2.4
3.2 Dis
tance
(m
iles)
Time (hours)
Jen’s Walking Rate
6543210
0 .25 .50 .75 1
(0.75,2.4)
(1,3.2)
Core Lesson
Graphs of Equivalent Rates:
Begin at the Origin
Form a Straight Line
In this lesson you have learned how to determine if two rates are equivalent by graphing.
Guided Practice Let x = parts of yellow Let y = parts of blue Graph the data in the table to determine which green paint mixtures have equivalent ratios of x:y
Paint Parts of Yellow Parts of Blue
A 1 2
B 2 3
C 3 6
D 4 6
E 5 8
F 6 9
Guided Practice
0 1 2 3 4 5 6 70123456789
10
Green Paint Mixtures
Blue
Yellow
A (1,2)B (2,3)
C (3,6)
D (4,6)
F (6,9)E (5,8)
Guided Practice Compare Ratios of Parts Yellow : Parts Blue
A & C =
1:2
0
1
B, D & F = 2:3
0
1
E = 5:8
0
1
Extension Activities
Create three shades of green paint by mixing different parts of yellow and green paint. Record the parts of yellow and green that you used in a table. Graph the data from your table. Write three equations for your green paint mixtures.
Extension Activities
Paint Parts of Red Parts of Yellow
A 2 0
B 4 2
C 3 3
D 3 6
E 0 1
Create the following paint mixtures. List the paints from the most red to the most yellow.
Quick Quiz Let x = parts of red y = parts of blue
Graph the data in the table to determine which purple paint mixtures have the same ratio?
Paint Parts of Red Parts of Blue
A 1 6
B 2 8
C 3 18
D 4 24
E 5 20
F 6 18