10. The graph represents the distance travelled when Liz took her dogs, Coco and Fudge, for a walk.


Use the graph to answer the following questions. (i) How far is Liz from home at point B ? (ii) How long does it take Liz to reach point C ?


(iii) What is happening between point B and point C ? Justify your answer.


(iv) During which part of the walk are Liz and her dogs walking fastest? Justify your answer.


11. The graph shows the distance travelled by three diff erent objects in a certain time. Which of the three objects is travelling the fastest?


Justify your answer with mathematical calculations. y 12


10 8 6 4


2 00 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0


x


y


1 000 500


A B C


125 250 375 500 Time (s)


Remember: Speed is a rate of change. B C A x


D


9.4 Parallel and perpendicular lines Slopes of parallel lines


Discuss and discover


Work with a classmate to complete the following activity. In the diagram, the line AB is parallel to the line CD . (i) Find the slope of the line AB . (ii) Find the slope of the line CD . (iii) What do you notice?


(iv) Construct two more pairs of parallel lines on graph paper and investigate the relationship between the slopes of these lines.


(v) Write a general statement about the relationship between the slopes of parallel lines.


If two lines are parallel, their slopes are equal. If l1


∥ l2 then m1 = m2


In the diagram shown, the two lines are parallel. Therefore, their slopes are equal: 3


__ 1 = 3


m1 170 Linking Thinking 2


__ 1


= m2 y


4 5 6


3 2 1


–1 0 1 2 3 A y


3 2 1


–5 –4 –3 –2 –1–1 0


C


–2 –3 –4


Slope = 3 l1


__ 1


l2 Slope = 3


__ 1


4 x B D 1 2 3 4 5 x


By the end of this section you should be able to: ● work with parallel and perpendicular lines


Distance (m)


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