Questions

Use this set of questions to test your knowledge on proportion, ratio and graphs.

Exercise

1. Which of these number pairs are in proportion and which are not? Convince a friend.
   1. (12, 3), (20, 4)
   2. (6, 48), (21, 168)
   3. (5, 15), (10, 20)
   4. (28, 7), (96, 24), (16, 4)
2. A photograph is 150 mm by 100 mm. Which of the following gives the dimensions of an accurate enlargement of the photograph?
   1. 450 mm by 350 mm
   2. 375 mm by 250 mm
   What is the scale factor of the enlargement (i.e. the constant of proportionality)?
3. In each of these examples the relationship between y and x is linear; that is, as x changes, y changes at a constant rate. In each case, state the rate of change and determine whether y is proportional to x.

   1. x	1	2	3	4	5 …
      y	6	10	14	18	22 …

   2. x	1	2	3	4	5 …
      y	0.2	0.4	0.6	0.8	1 …

   3. x	1	2	3	4	5 …
      y	12	10	8	6	4 …

   4. x	5	10	15	20	25 …
      y	8	16	24	32	40 …

   Plot graphs for each of these relationships and relate the features of your graphs to what you have discovered. For each of the examples, can you find an equation connecting y and x?
4. Which of the following situations are examples of direct proportion and which are not?
   1. Cost of purchasing a given quantity of tomatoes at £1.38 per kilogram.
   2. Distance travelled on a bicycle in a given time, at a steady speed of 15 mph.
   3. Number of dollars you can purchase for your money, at the rate of $1.45 for every pound sterling, together with a flat rate commission of £5 per transaction.
   4. Table of distances in miles converted roughly into kilometres.

Answers to exercise

1. 1. No, because $\frac{12}{3}=4$ and $\frac{20}{4}=5$
   2. Yes, because $\frac{6}{48}=\frac{21}{168}=\frac{1}{8}$
   3. No, because $\frac{5}{15}=\frac{1}{3}$ and $\frac{10}{20}=\frac{1}{2}$
   4. Yes, because $\frac{28}{7}=\frac{96}{24}=\frac{16}{4}=4$
2. 1. No, because $\frac{450}{150}=3$ and $\frac{350}{100}=3.5$
   2. Yes, because $\frac{375}{150}=\frac{250}{100}=2.5$
      Scale factor of enlargement is 2.5
3. • 1. $m=4$ (y changes by 4 for every 1 of x). Not a proportion, because $\frac{6}{1}=6$, $\frac{10}{2}=5$, etc.
     2. $m=0.2$. A proportion, because $\frac{0.2}{1}=\frac{0.4}{2}=\dots =0.2$
     3. $m=-2$. Not a proportion, because $\frac{12}{1}=12$, $\frac{10}{2}=5$, etc.
     4. $m=\frac{8}{5}$ (y changes by 8 for every 5 of x, or by $\frac{8}{5}$ for every 1 of x). A proportion, because $\frac{8}{5}=\frac{16}{10}=\dots =1.6$
   • Equations are
     1. $y=4x+2$
     2. $y=0.2x$
     3. $y=14-2x$
     4. $y=\frac{8x}{5}$
4. 1. Yes – cost of tomatoes is proportional to quantity purchased.
   2. Yes – distance travelled is proportional to the time on the journey.
   3. No – because of the fixed charge of £5 (but it is a linear relationship).
   4. Yes – distance in kilometres is proportional to distance in miles.