Compare Two Proportional Relationships

Check who is faster and write by how much: reduce each representation to its unit rate, then compare those, and say how.

ExampleAva’s reading rate:

x (days)	2	4	6
y (pages)	60	120	180

Dev’s reading rate is given by y = 26x.

Who reads faster, and by how much? Explain how you compared two different representations.

AvaDev by 4 pages per day

Why? each unit rate is the slope: Ava 30 and Dev 26 pages per day (from the table, divide any y by its x: 60 ÷ 2 = 30); a table, an equation and a graph all reduce to that one number, which is what makes them comparable

1.Ava’s pay rate is given by y = 24x.Dev’s pay rate:
x (hours) 2 4 6
y (dollars) 38 76 114
Who earns faster, and by how much? Explain how you compared two different representations.
AvaDev by
Why?
2.Ben’s reading rate is given by y = 24x.Dev’s reading rate:
x (days) 2 4 6
y (pages) 26 52 78
Who reads faster, and by how much? Explain how you compared two different representations.
BenDev by
Why?
3.Chloe’s speed:
x (hours) 2 4 6
y (km) 32 64 96
Elena’s speed is given by y = 14x.
Who cycles faster, and by how much? Explain how you compared two different representations.
ChloeElena by
Why?
4.Ava’s typing rate:
x (minutes) 2 4 6
y (words) 34 68 102
Finn’s typing rate is given by y = 18x.
Who types faster, and by how much? Explain how you compared two different representations.
AvaFinn by
Why?
5.Chloe’s typing rate is given by y = 16x.Finn’s typing rate:
x (minutes) 2 4 6
y (words) 22 44 66
Who types faster, and by how much? Explain how you compared two different representations.
ChloeFinn by
Why?

x (hours)	2	4	6
y (dollars)	38	76	114

x (hours)	2	4	6
y (km)	32	64	96

x (minutes)	2	4	6
y (words)	34	68	102

x (minutes)	2	4	6
y (words)	22	44	66