PROPORTIONAL AND NONPROPORTIONAL SITUATIONS WORKSHEET

Question 1 :

The graph shows the relationship between the weight of an object on the Moon and its weight on Earth. Explain why this relationship is proportional and also write an equation for the relationship.

Question 2 :

The entrance fee for Mountain World theme park is $20. Visitors purchase additional $2 tickets for rides, games, and food. The equation y = 2x + 20 gives the total cost, y, to visit the park, including purchasing x tickets. Explain  why the relationship between number of tickets and total cost is not proportional using a graph.

Question 3 :

The relationship between two quantities is linear. How can you conclude from the graph whether the relationship is proportional or non proportional?

Use a graph to tell whether x and y are in a proportional

Question 4 :

Question 5 :

Question 6 :

The graph shows that the distance traveled by the Mars rover Curiosity is proportional to the time traveled. Interpret each plotted point in the graph.

Tell whether x and y are in a proportional relationship. If so, find the unit rate.

Question 7 :

Question 8 :

Let y be the temperature x hours after midnight. The temperature is 60°F at midnight and decreases 2°F every 1/2 hour.

Question 9 :

You pay $1 to rent a movie plus an additional $0.50 per day until you return the movie. Your friend pays $1.25 per day to rent a movie.

a. Make tables showing the costs to rent a movie up to 5 days.

b. Which person pays an amount proportional to the number of days rented?

1. Answer :

Step 1 :

The graph of the given relationship contains the origin or the line is passing through the origin.

So,  the relationship is proportional.

Step 2 :

Make a table relating amount earned to number of hours.

Step 3 :

Find the constant of proportionality.

Moon weight : Earth weight

1 : 6 = 1  : 6

2 : 12 = 1  : 6

3 : 18 = 1  : 6

5 : 30 = 1  : 6

The constant of proportionality is 1 : 6 or 1/6.

Step 4 :

Write an equation.

Let x represent weight on Earth.

Let y represent weight on the Moon.

The equation is y = kx.

Replace k with 1/6 in the above equation.

y = (1/6)x

y = x/6

2. Answer :

Step 1 :

Choose several values for x that make sense in context.

Step 2 :

Plot the ordered pairs from the table. Describe the shape of the graph.

Step 3 :

In the above graph, the points lie on a line. But the line does not pass through the origin. So, the relationship between number of tickets and total cost is not proportional.

3. Answer :

If the relationship between the two quantities is linear, its graph will be a line.

If the line goes through the  origin, then the relationship is proportional.

If the line does not go through the  origin, then the relationship is non proportional.

4. Answer :

Step 1 :

From the table, by observing the points. We get (2, 6) (4, 8) and (6, 8).

Step 2 :

Plotting these points on the graph.

Step 3 :

By observing the graph, since the line doesn't pass through origin. It must be non proportional relationship.

5. Answer :

Step 1 :

From the table, by observing the points. We get (1, 2) (2, 4) and (3, 6)

Step 2 :

Plotting these points on the graph.

Step 3 :

By observing the graph, the line passes through origin. Then it is proportional relationship.

6. Answer :

The graph shows the proportional relationship.

(0, 0) : The rover travels 0 inches in 0 seconds.

(1, 1.5) : The rover travels 1.5 inches in 1 second. So, the unit rate is 1.5 inches per second..

(3, 4.5) : The rover travels 4.5 inches in 3 seconds. Because the relationship is proportional. We can find the unit rate.

= 4.5 in/3 sec

= 1.5 in/1 sec

(or)

= 1.5 inches per second

7. Answer :

The points from the table are (1, 5) (4, 20) (7, 35) and (10, 50).

• (1, 5) : For every one hour 5 feet.
• (4, 20) : For every fours hours 20 feet
• (7, 35) : For every seven hours 35 feet.

It is a proportional relationship.

Rate of change = 5 / 1

= 5 feet per hour.

8. Answer :

Let y be the temperature x hours after midnight. The temperature is 60°F at midnight and decreases 2°F every 1/2 hour.

Let y be the temperature and x be the number of hours.

Initial temperature = 60°F

Every half an hour the decrease is 2°F, then for one hour the decrease will be 4°F.

y = 60 - 4x

It is not a proportional relationship.

You pay $1 to rent a movie plus an additional $0.50 per day until you return the movie. Your friend pays $1.25 per day to rent a movie.

Let x be the number of days.

Let y be the amount i pay.

y = 1 + 0.50x

Amount paid by my friend :

y = 1.25x

It is a proportional relationship.

b) Your friend pays the amount in proportional relationship.

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