Unit 6 Day 4 Graphing Proportional Relationships

Unit 6 Day 4
Graphing Proportional Relationships

What does a proportional relationship look like when it is graphed on a coordinate plane?

Since the ratios in proportional relationships are all equivalent, the graph of the relationship is a straight line with no 'turns' or changes in direction. You should be able to connect all the points with a ruler, starting at (0, 0).

The graph is 1, continuous straight line

In any proportional relationship, if one value or part of the ratio is 0, the other has to be 0, also. Therefore, if you graph the points in a proportional relationship, the line should start at the origin (0, 0).

The graph starts at (0, 0)

Multiple Select

Choose all the graphs below that show a proportional relationship.

Graphing Ratios

Write the correct units (money, miles, number of people, etc.) next to each axis. Remember that the x-axis goes side-to-side and the y-axis goes up-and-down.

Label your axises

If you are using a table or chart to graph points, first label which are the x values and which are the y values. Remember that ratios are y/x, so whichever units would come first in your unit rate are the y values.

Identify x and y

Labelling

The graph shows the cost of different amounts (in ounces) of frozen yogurt. For example, 2 ounces of yogurt costs $4. Label the x and y axis appropriately with the units.

Drag labels to their correct position on the image

ounces of frozen yogurt

price ($)

Reading Graphs

On the graph, the unit rate is where the x-value is 1. The point labeled A is the unit rate. It is (1, 14), and it means that this person earns $14 per 1 hour.

Unit Rate

Ordered pairs are written as (x, y). The point labeled B on the graph is (2, 28). To get to point B, we go over/right 2 and then up 28.

(x, y)

C

A

B

Dropdown

The graph shows the cost of different amounts (in ounces) of frozen yogurt. The point (3, 6) on the graph means that ​

Select answer

ounces of frozen yogurt costs ​

Select answer

dollars.

Labelling

The graph shows the cost of different amounts (in ounces) of frozen yogurt.

Label the unit rate on the graph with the correct ordered pair.

Label the point that shows the cost of 5 ounces of frozen yogurt with the correct ordered pair.

Drag labels to their correct position on the image

(5, 10)

(0, 0)

(10, 5)

(2, 1)

(1, 2)

(2, 4)

Multiple Choice

The graph shows the total cost of gasoline based on how many gallons of gasoline are purchased. Which of the following answer choices correctly identifies a point on the graph and explains what it means in the context of this situation?

• (4, 10) means that 4 gallons of gasoline costs $10

• (10, 4) means that 4 gallons of gasoline costs $10

• (4, 10) means that 10 gallons of gasoline costs $4

• (10, 4) means that 10 gallons of gasoline costs $4

What if the unit rate isn't labeled?

Sometimes, it isn't very clear what point on the graph is the unit rate because the unit rate is not a whole number. On the graph shown here, we can see where x is 1, but it isn't clear what the y-value is at that point.

If this happens, we can find the unit rate by using any other point that is clear and dividing y/x.

​Unit Rate

​We know the point (4, 10) is in this proportional relationship. 10/4 gives us a unit rate of 2.5. Therefore, the point on this graph that represents the unit rate is (1, 2.5). This means that it costs $2.50 per gallon of gasoline.

Multiple Choice

What ordered pair on the graph shows the unit rate for helicopter A?

• (2, 5)

• (1, 2.5)

• (3, 4)

• (1, 1.3)

Multiple Choice

What is the unit rate of helicopter B?

• Helicopter B flew 4 meters in 3 seconds.

• Helicopter B flew 5 meters in 2 seconds.

• Helicopter B flew $$1\frac{1}{3}$$ meters in 1 second.

• Helicopter B flew $$2\frac{1}{2}$$ meters in 1 second.

Multiple Choice

Choose the answer that correctly identifies and describes a point on the graph for helicopter A.

• (6, 15) Helicopter A flew 15 meters in 6 seconds.

• (6, 15) Helicopter A flew 6 meters in 15 seconds.

• (9, 12) Helicopter A flew 12 meters in 9 seconds.

• (15, 6) Helicopter A flew 15 meters in 6 seconds.

Making Predications

We can also use the graph of a proportional relationship to make predictions and find other ratios in the relationship.

We can use the unit rate in the same way we have when we were given a table of values.

​Example: How much would 20 hours cost?
We see the point (2, 100) is in this proportional relationship. That means that it costs $100 for 2 hours. The unit rate is 100/2 = $100 per hour.

​By cross multiplying to solve for y, we get that 20 hours would cost $1000.

Multiple Choice

This graph shows the cost of cheese (in British pounds) based on the amount of cheese being purchased (in kg). Using the graph, how much would it cost for 10 kg of cheese?

• 80 pounds

• 1 pound

• 8 pounds

• 1.25 pounds

Multiple Choice

This graph shows the cost of cheese (in British pounds) based on the amount of cheese being purchased (in kg). What is the unit rate and what does it mean in this context?

• (5, 40) This means 5 kg of cheese costs 40 British pounds.

• (5, 40) This means 40 kg of cheese costs 5 British pounds.

• (1, 8) This means 1 kg of cheese costs 8 British pounds.

• (8, 1) This means the cheese costs 8 British pounds per 1 kg.