Proportional Graphs
Common Core Standard: Explain what a point (x, y) on the graph of a proportional relationship means in terms of the
situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.

Proportional relationships form straight lines through the origin on a graph

The unit rate is shown in the graph where the x-coordinate equals 1,on the line, the y-coordinate is the unit rate
(constant of proportionality)

However, every other point on the line means something in terms of the proportional relationship

Example: The proportional graph below shows the number of coffee grounds used in cups of coffee. Using the
graph, determine the unit rate and determine how many grounds are used in 3 cups of coffee.
]
o
o
1st: What do x and y represent in the graph?

x represents the cups of coffee, because the c ups are along the x-axis

y represents the coffee grounds, because the grounds are along the y-axis
The unit rate is where x = 1; at this location on the line, the y-coordinate is 2.5. So, there are 2.5 grounds
per cup of coffee.
o
Looking at where x =3 for 3 cups of coffee, the y-coordinate is 7.5. Thus, in 3 cups of coffee there are 7.5
coffee grounds.

Sometimes, the unit rate is not a whole number.

Example: The graph below shows a cell phone company’s basic plan. Determine the unit rate.
o
Looking at the graph, one point that is easy to see is (140, 10)
o
x is the number of texts and y is the cost
o
To determine the unit rate, the x-coordinate needs to equal 1
o
So, divide 140 by 140 to get 1
o
Divide 10 by 140, because this a proportional relationship, and both numbers must have the same process
done to them to remain proportional
o
10 ÷ 140 = approximately 0.07
o
So, the unit rate is $0.07 per text message