# Lesson Worksheet: Modeling with Straight Lines Mathematics

In this worksheet, we will practice modeling real-world examples on linear equations.

Q1:

The graph shows the relationship between the radius and the circumference of a circle in centimetres. Are the variables proportional? • AYes
• BNo

Q2:

A hiker is walking along a mountain trail and records the distance they have walked at various time intervals, as shown below.

 Time (min) Distance (km) 30 45 60 70 90 2 3 4 5 6

By drawing a graph, determine whether the data can be approximated by a linear model.

• AYes, the data can be approximated by a linear model.
• BNo, the data cannot be approximated by a linear model.

Q3:

The population of a village is counted every ten years and varies according to the table below.

 Year Population 1990 2000 2010 2020 570 630 740 980

Can the data be approximated by a linear model? Draw a graph to help you determine the answer.

• AYes
• BNo

Q4:

In an online game, it is possible to buy 5 loot boxes for 3.15. Assuming a flat rate between the number of crates bought, , and price, , write an equation linking and in the form or , where is approximated to two decimal places if needed.

• A
• B
• C
• D
• E

Q5:

Charlotte collects identical samples, places them in a dish, and weighs the dish on a scale. She plots the weight for various numbers of samples. Write an equation linking the weight to the number of samples in the form .

• A
• B
• C
• D
• E

What is the physical significance of the value of ?

• AIt is the weight of the dish in grams.
• BIt is the weight of an individual sample in grams.
• CIt is the combined weight of a dish and 1 sample in grams.
• DIt has no physical meaning.
• EIt is the combined weight of 5 samples in grams.

Q6:

A construction company charges fees based on the number of days spent on a job, with an added flat rate on the first day. One job takes 7 days and costs £9,175, while another takes 13 days and costs £15,325.

Write an equation linking the number of days spent to the cost (in £) in the form .

• A
• B
• C
• D
• E

What real-world meaning does have in the equation?

• AIt is the cost per day in £.
• BIt is the cost of the flat rate in £.
• CIt is the total cost in £ minus the flat rate.
• DIt is the cost of 7 days in £.
• EIt is the total cost in £ divided by the number of days.

Q7:

Anthony went on vacation. The graph represents the amount of money he spent there. Determine the amount he spent daily. Q8:

The graph below represents a relation between the time in hours and the amount of fuel in a car tank in liters. Determine the amount of fuel remaining after 15 hours of driving and the amount of fuel consumed per hour. • AThe amount of remaining fuel is 36 liters and the amount of fuel consumed is liters per hour.
• BThe amount of remaining fuel is liters and the amount of fuel consumed is liters per hour.
• CThe amount of remaining fuel is 24 liters and the amount of fuel consumed is liters per hour.
• DThe amount of remaining fuel is 24 liters and the amount of fuel consumed is liters per hour.

Q9:

A scuba diver is ascending from their dive at the rate shown in the diagram. Assuming they continue at the same rate, how much time will have passed when they reach the surface?

• A5 minutes and 30 seconds
• B3 minutes
• C4 minutes
• D4 minutes and 30 seconds
• E5 minutes

In the last part of the ascent, they decide to slow their rate of ascent to 5 meters per minute. Given that this is the case, how much time will have passed when they reach the surface?

• A5 minutes
• B4 minutes and 36 seconds
• C5 minutes and 12 seconds
• D4 minutes
• E4 minutes and 48 seconds

Q10:

A scientist records the data for two variables, and , on a scatterplot, as shown below. Which of the following linear equations best approximates the relationship between the variables?

• A
• B
• C
• D
• E

According to this approximation, at what value of will the two variables be equal?

Hint: Approximate to one decimal place if needed.