Linear relations

Exercise 1

Cyclist $1$ cycles at a constant speed of $20$ km/h from A to B. Cyclist $2$ cycles at a constant speed of $25$ km/h from B to A. The distance between A and B is $150$ km for both cyclists. $a$ represents the distance from A and $t$ represents the time in hours.

a

In a $a, t$ -coordinate system draw the corresponding graphs of both cycle trips.

b

For both cyclists give a formula describing the relation between $a$ and $t$ .

c

How much time has passed when the two cyclists meet each other? Explain your answer.

Exercise 2

Calculate the points of intersection with the axes for the linear functions below. Then draw the corresponding graphs using the y-intercept and gradient. Use the graphs to check the points of intersection with the axes.

a

$y_{1} = 3 x - 5$

b

$y_{2} = x - 4$

c

$y_{3} = - 0.5 x + 4$

d

$y_{4} = - 2 (x + 3)$

Exercise 3

Renting a specific type of car from a car rental company will cost you
$g = 75 + 0.09 \cdot k$ per week.
Here $k$ is the number of kilometers you will drive and $g$ the costs in €.

a

The car rental company asks for a standing charge per week. How much is that charge?

b

How much do you pay per kilometer you will drive?

c

Write down the formula for the costs of another rental car which has a standing charge which is €12,50 higher per week, and costing $10$ cents per kilometer.

Exercise 4

Look at the table below:

hours worked `u`	0	2	5	9	10
costs `k`	65	135	240	380	415

a

Explain why there is a linear relation between $k$ and $u$ . Also explain why $k$ is not directly proportional to $u$ .

b

Which of these formulas correspond to the table?

$k = u + 65$

$k = 35 u + 65$

$k = 65 u + 70$

c

Use the correct formula to calculate the costs when the work has taken $6$ hours.

d

Use the correct formula to calculate the costs when the work has taken $2$ hours and $50$ minutes.

Exercise 5

The profit $p$ (in €) made during a party night depends on the number of visitors $n$ . The formula is given as: $p = 2.5 \cdot n - 300$ .

a

Calculate the profit when the number of visitors is $200$ .

b

What could be the reason for the number $- 300$ in this formula?

c

What does the number $2.5$ represent?

Exercises