4.10 Interpreting proportional relationships
For each of the following graphs, describe what the plotted point represents:
The graph shows the price for playing arcade games.
The graph shows the number of eggs a farmer's chickens lay each day.
The graph shows the amount of time it takes Kate to make beaded bracelets.
The graph shows the number of liters of gas used by a fighter jet per second.
The graph shows the number of liters of ice cream per tub.
The graph shows the distance Natalia swam per minute.
The number of fish caught by Harry last weekend is shown on the graph:
State what the point on the graph represents.
How many fish would Harry expect to catch in 1 hour?
The amount of chocolate and milk that can be heated up together to make a hot chocolate is shown on the graph:
State what the point on the graph represents.
How many spoons of chocolate should be mixed with 1 cup of milk?
The number of cupcakes eaten by guests at a party is shown on the graph:
State what the point on the graph represents.
Danielle is having a party and expects to have 10 guests. According to the rate shown on the graph, how many cupcakes should she buy?
The amount of coffee beans needed to make an espresso is shown on the graph:
State what the point on the graph represents.
How many grams of coffee beans are needed to make an ounce of espresso?
Heavy rainfall has resulted in flooding of some roads. The water level has been monitored on a particular road as shown in the table:
| \text{Number of hours} \left(t\right) | 0 | 0.5 | 1 | 1.5 | 2 |
|---|---|---|---|---|---|
| \text{Water level in inches} \left(x\right) | 0 | 0.75 | 1.5 | 2.25 | 3 |
Is the water level proportional to the number of hours passed?
Write an equation relating x and t.
After 2 hours of rainfall, authorities make a decision to close the road when the water level reaches 7.5 \text{ in}. If it continues to rain at the same rate, how much longer do residents have to access the road before it closes?
The cost of parking for various amounts of time was recorded at 4 different locations in the city. The following table summarizes the results:
| \text{Number of hours} \left(x\right) | 3 | 3.5 | 12 | 8 |
|---|---|---|---|---|
| \text{Cost of parking} \left(y\right) | \$13.50 | \$16.75 | \$54.00 | \$34.50 |
Find the cost per hour at the location where parking cost \$13.50.
Is x proportional to y? Explain why this might be.
During a group gym session, participants need to do "double unders" skipping for 10 minutes. Those who can’t do double unders are given the option of doing single skips, but they must do more. The table shows the pattern of how many double under and single skips participants had to do for the first 4 minutes.
| \text{Time} \left(t \text{ minutes}\right) | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| \text{Double under skips} \left(x\right) | 19 | 38 | 57 | 76 |
| \text{Single skips} \left(y\right) | 76 | 152 | 228 | 304 |
Is the number of double under skips proportional to the number of minutes?
Write an equation for x, the number of double under skips done in t minutes.
How many double under skips did participants do in 10 minutes?
For participants who did single skips, how many single skips counted as 1 double under skip?
Write an equation relating x, the number of double under skips, to y, the number of single skips.
How many single skips did participants have to do in 10 minutes?
A car dealership has received 88 of the latest model Subaru. The dealership hopes to have sold all of them within 11 weeks. The number sold by the end of the second and fourth weeks is shown in the table:
| \text{Week} \left(w\right) | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| \text{Number of cars sold} \left(n\right) | 12 | 24 |
Assuming the new Subarus are being sold at a constant rate, complete the table.
Write an equation relating w, the number of weeks passed, and n, the number of cars sold.
If the new models continue to be sold at this rate, how many will be sold in 11 weeks?
How many of the new models will remain after 11 weeks?
How many new models would they have had to sell each week to have had them all sold in 11 weeks?
The original photo measures 8.5\text{ cm} in width and 34\text{ cm} in length. When a customer wants to print a copy in a different size, the width and length must be in the same ratio as the original so that the photo does not appear distorted.
If x represents the width and y represents the length of the printing size, write the equation for y in terms of x.
Find the length of a copy if the width of the copy is 13 \text{ cm}.