Linear relations

Exercise 1

a

Own answer

b

Cyclist A: $a = 20 t$
Cyclist B: $a = 150 - 25 t$

c

Cyclist A.

d

$t = 3 \frac{1}{3}$ hours

Exercise 2

a

Not directly proportional

b

Directly proportional; constant of proportionality is $3$ .

c

Not directly proportional

d

Directly proportional; constant of proportionality = $\frac{1}{3}$ .

e

Directly proportional; constant of proportionality = $\frac{1}{3}$ .

f

Directly proportional; constant of proportionality = $- \frac{1}{3}$ .

Exercise 3

a

Yes.

b

No.

c

Not necessarily. If you had covered no distance at all at $t = 0$ , it is.

d

No, the speed increases all the while, so the distance travelled per second changes.

e

Yes, in similar rectangles the ration of length and width remains the same.

f

No.

Exercise 4

a

$K = \frac{71}{600} a$

b

$K = \frac{11}{200} a$

c

From $22106$ km per year. Use your graphic calculator to find the first value of a where more than $1400$ euros difference between both values for $K$ occurs.

Exercise 5

a

The call-out charge is not included in the wages.

b

The call-out charge is now included.

c

$T K = 22.50 u + 30$

Exercise 6

a

$26$ km in $45$ minutes converts to $34 \frac{2}{3}$ km/h.

b

$a = 34 \frac{2}{3} t$

Solutions to the exercises