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Coordinate Geometry

1. Write the coordinate of these points.A __________

B __________

D __________

2. Draw a line on the grid showing these slopes. Label lines clearly.a) Slope of4

b) Slope of 35

c) Slope ofzerod) Undefined slope

3. For the interval joining points A and C, find:Distance (length)

midpoint

slope

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4. Find the slope of these intervals.A _______________ B _______________

C _______________ D _______________

5. Find the midpoint of the interval joining (-9, 4) and (1, -7)

6. Find the length of the interval joining (9, -3) and (-5, -7)

7. Find the slope of the interval joining (0, -4) and (-6, 3)

Linear Equation and Models

8. State the slope and y-intercept of the line represented by these equations:a) 5 1y x slope __________________ y-intercept______________b) 3 2y x slope __________________ y-intercept______________c) 8x slope __________________ y-intercept______________d) 2x 3y = 5 slope __________________ y-intercept______________

9. Find the equation of these lines on the graph.1 _________________________

2 _________________________

3 _________________________

4__________________________

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10. Write the equations of these lines.a) The line has a y-intercept of 16 and a slope of -7.

b) The line passes through (0, -4) and has a slope of 9

c) The line passes through the points (0, 6) and (12, 0)

d) The line passes through the points (5, -1) and with a slope of 8

e) The line passes through the points (2, 8) and (-6, 6)

11. a) Is this a linear model? Explain how you can tell.

b) State the y-intercept of the line.

c) Find the slope of the line.

d) Hence, find the equation of the line represented by this table of values.

Challenge

12.Find the equation of a line passing through the point (2, 5) and parallel to the line y = 7

13. Find the equation of a line passing through the point (-3, 8) and parallel to the line x 2y = 6

x -1 0 1 2 3 4 5

y 12 10 8 6 4 2 0

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14. Karim fill his cars petrol tank up with 180 Liters of petrol. Each day he uses 2 litres of petrol going to woHe wants to know how much petrol he has in his car.

Identify the independentand dependentvariables in this relationship.

Construct a table-of-values to represent how Jeremy savings is changing.x 0 1 2 3 4 5

y

Does this table represent a linear relationship? Explain why/why not

Will the slope be positive or negative? Explain how you can tell from the table-of-values.

Graph the data on the axes below (set up suitable axes)

What is the slope of the graph?

What is the y-intercept and what does it represent in this context?

Find the equation that models this scenario.

Use the equation to find how much petrol Karim has in the tank after 19 days.

Use the equation to find how many days is takes for Karim to have only 16 litres of petrol left.

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Part B Answer in the space provided

1. Here is the cross section of a house. It is getting a new roof built on the house. There are a few more calculathe builders need to do before they can finish.

a) The beamsAB and BCneed to be equal in length. Can you prove this for the builder? (3 marks

b) Find the coordinates of the point D where the support beam from B meets the cross beamAC.(1 ma

c) How long is the support beam BD? (1 mar

d) The final part of the roof construction is the addition oftwo metal trusses to support the beamsAB and BCThe base of the two trusses will be placed at point D and reachAB at its midpoint M and reach BCat its poin

Draw the two trusses on the diagram, clearly labeling M and Nand determine the coordinates of M and N.

(3 mark

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2 1 0 1 2 3 4 5 6 7 8600

660

720

780

840

900

960

1020

1080

1140

1200

1260

1320

1380

1440

1500

1560

1620

1680

1740

1800

x

y

2. Jeremy is saving for an IPOD. He already has P1200 saved. To earn money, he sells lemonade on the weekfor P60 per cup.

a) Which is the independent variable (x)? _____________________________Which is the dependent variable (y)? ______________________________ (2 marks)

b) Construct a table-of-values to represent how Jeremy savings is changing. (2 max 0

y 1200

c) Does this table represent a linear relationship? Explain why/why not. (2 ma

d) Will the slope be positive or negative? Explain how you can tell from the table-of-values. (2 ma

e) Graph the table-of-values on the grid. (2 m

f) Determine the slope of the graph. What does the slope represent in context of the scenario?(2 mar

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g) Determine the equation of the line.(2 ma

h) How much will Jeremy have saved after selling 85 cups of lemonade? Show your work.

(2 ma

i) How many cups of lemonade will Jeremy need to sell to have saved the P 15 000 for the IPOD?Show your work.

(2 ma

THE END

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