4. Copy the table below and match the slope to the line. Give a reason for each answer. Slope Line


Reason (i)


_ 4


1 E


(ii) − 2 (iii)


(iv)


0 3


(v) − 5 _


6 5. The diagram shows a ramp and a hill. 6 m Ramp 8 m 6 m Ramp 8 m 12 m Hill 8 m 12 m


Do you think it would be more diffi cult, considering the steepness of each, to walk up the ramp or the hill? Explain your answer using mathematical calculations.


6. Use your knowledge of the slope of a line to investigate if the points A ( − 2, − 1 ) , B ( 1, 5 ) and C ( 4, 11 ) are collinear (lie on the same line).


7. The Murphy family go on a driving holiday in America. The graph shows the cost of the driving portion of the holiday.


(i) Use the graph to fi nd the slope of the line.


(ii) Explain the meaning of the slope in the context of this question.


Cost $


2·40 1·20 0


y Hill 8 m D C B x y A


0


8 16 24 32 Km driven


8. Patrick’s Hill in Cork City is claimed to be one of the steepest streets in Ireland. It has an ascent of approximately 40 metres over a horizontal distance of 250 metres.


(i) Calculate the average slope of Patrick’s Hill.


Baldwin Street, Dunedin in New Zealand holds the Guinness World Record for the steepest street in the world. It has an ascent of approximately 68.6m over a horizontal distance of 343 m.


(ii) Calculate the average slope of Baldwin Street. (iii) Which street is steeper? Justify your answer.


9. Planners designing a mountain biking course must ensure that the slope (ignoring its sign) is between 0 ⋅ 1 and 0 ⋅ 4 for safety reasons. The graph shows the slopes of various sections of the proposed mountain biking course.


(i) Show that the section from B to A does not pass the safety requirements.


(ii) A course going from A to C to D to E to B is proposed. Investigate if each section of this course passes the safety requirements.


B Section A Applying our skills 169 y A x C D


x


E


9 Working with the coordinate plane


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