Practice questions 9.6


1. The initial height of a liquid in a glass cylinder is 5 cm. As liquid is added the height increases by 2 cm per minute. (i) Create an equation to show how the height of the liquid increases over time. (ii) What will be the height of the liquid after 4 minutes? (iii) After how many minutes will the height of the liquid be 17 cm? (iv) Draw a graph showing how the height of the liquid changes over 10 minutes. (v) Does your graph represent a linear function? Justify your answer.


2. Fiona’s offi ce has recycled 3 kg of paper so far this year. The new recycling plan aims to have the offi ce recycling 2 kg of paper each week.


(i) Create an equation to show how much paper will be recycled over time. (ii) What is the total amount of paper that the offi ce will have recycled after 6 weeks? (iii) After how many weeks will the offi ce have recycled 15 kg of paper? (iv) Draw a graph to show the total amount of paper the offi ce has recycled in 10 weeks. (v) Does your graph represent a linear function? Justify your answer.


3. A puppy named Snowball was born weighing 500 g. He then gained 1 kg every month for a year. (i) Create an equation to show how much weight Snowball gains over time. (ii) What weight will Snowball be in kg after 7 months?


(iii) Draw a graph to show how much weight in kg Snowball gains over 10 months.


(iv) From your graph, estimate Snowball’s weight in kg after 3⋅5 months. (v) Does your graph represent a linear function? Justify your answer.


4. A taxi company charges a €2 pick-up fee, plus an additional €3 per kilometre driven. (i) Create an equation to show how the cost of the taxi rises with the distance travelled. (ii) How much will it cost to travel 9 kilometres? (iii) How far will I have travelled if my bill is €17? (iv) How many kilometres is a taxi ride that costs €32? (v) Draw a graph to show how much a taxi would charge for a 23-kilometre journey. (vi) Does your graph represent a linear function? Justify your answer.


5. A bucket contains 1 litre of water. The bucket develops a small leak in the base and loses 150 ml (millilitres) of water every minute.


(i) Create an equation to show the rate at which the volume (amount) of water is decreasing in the bucket.


(ii) How many millilitres of water has the bucket lost after 4 minutes? (iii) Draw a graph showing the loss of water over 6 minutes. (iv) Is your graph linear? Justify your answer.


(v) Using your graph, determine how many minutes will pass until the bucket is completely empty.


(vi) Create and solve an equation to show how much time will pass until the bucket has 250 ml remaining.


Section A Introducing concepts and building skills


153


9 Solving linear relations


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