Linear Relations Review

Multiple Choice

  1. Maya’s Trip to School

• Maya walks to her friend Kadeem’s house, which is halfway between her home and the school. EQME10635

• They stay at Kadeem’s house for a few minutes, until Maya remembers that she has forgotten her lunch.

• Maya runs back home to get her lunch.

• When she gets home, her mother drives her to school so that she will not be late.

Which graph most accurately represents Maya’s trip to school?

  1. Koshen is creating his own summer gardening job. For each garden, he will charge a $10 initial consultation fee plus $8 per hour. EWhich graph best represents Koshen’s earnings for each garden?

3.

4.

Long Answers

  1. Mia delivers the local newspaper. Her base pay is $5 per week, and she gets $0.25 per paper. Which of the points on the graph represents Mia’s pay for delivering 25 newspapers in a week?

  1. Makin’ a Profit!

Student council is planning a dance.

  1. The cost to hire a DJ is $300.
  2. Tickets are sold at $6 each.
  3. The profit is based on the amount received from the tickets sold minus the cost of the DJ.

Complete the table of values to show the profit based on the number of tickets sold.

Graph the data on the grid below.

  1. Rockin’ Radicals

The Radicals, a small high school band, recently signed a contract with a record label. Their earnings include a signing bonus plus an amount per CD sold, as shown in the table below.

Determine the amount of the signing bonus and the amount they receive per CD.

Show your work.

  1. Tyler belongs to a fitness club at the community centre. The graph below represents the relationship between the number of times he visits the club and his total monthly cost.

What type of variation is this relationship (direct or partial), and what is the initial value? Explain your reasoning.

Karl joins a fitness centre. The cost includes a one-time fee of $100 plus a monthly fee of $30. If C represents his total cost and n is the number of months. Write an equation represents this relationship.

  1. Let’s Go to a WaterPark!

Two water parks have different methods of determining the cost of a season pass. The equations for both parks are given below, where C is the cost of the pass and n is the number of visits.

Graph the costs for both water parks on the grid below.

Determine which water park has the lower cost for a season pass.

Justify your answer.

  1. Up in the Air

Madiha throws a ball into the air one time. The height of the ball above ground is measured at six different times. The table below shows the data that Madiha collects.

Determine whether the relationship represented by the table is linear or non-linear. Justify your answer.

  1. If a wheelchair ramp has a rate of change (incline) greater than 0.1, then it is considered unsafe.

Determine whether or not each of the following ramps is safe.
Show your work and explain your reasoning.

  1. Devin went for a bicycle ride. The graph below shows his trip.
    Note: Distance is the number of kilometres from home.

a)Calculate his speed during the first hour (AB) and the second hour (BC).
Show your work.

b)How does the speed between A and B compare with the speed between B and C?

c)Explain what segment CD tells you about Devin’s motion.

d)Which section of the graph shows that Devin was changing speeds? Explain.

e)What information can you determine from segment EF?

  1. Sketch the graph that is described in each story.

a)Begin 5 metres from the sensor.

Walk towards the sensor for 6 seconds at a steady rate of 1 metre in 2 seconds.

Stop for 5 seconds.

Run back to your starting position at a steady rate of 1 metre per second.

Stop.

b)Begin at the sensor.

Walk very slowly at a steady rate away from the sensor for 3 seconds.

Increase your speed and walk at this new speed for 3 seconds.

Stop for 3 seconds.

Walk very slowly at a steady rate towards the sensor for 3 seconds.

Gradually increase your speed to a run and go back to the sensor.