The document discusses using coordinate planes and axes to plot points and graphs. It explains that every point on a coordinate plane has an x-coordinate and y-coordinate. Various examples are given of plotting lines defined by equations on the same set of axes, such as lines where x + y = a constant or y = mx + b. A series of questions are also provided asking to plot multiple graphs defined by equations on the same set of axes.

1. TO DESCRIBE THE POSITION OF AN OBJECT WE CAN USE A SET OF AXES . Co-ordinates: ( 2 , 7 ) 2 along the x -axis , 7 along the y -axis . x = 2 , y = 7 Co-ordinates: ( -6 , 3 ) -6 along the x -axis , 3 along the y -axis . x = -6 , y = 3 x y

2. Every point has an x co-ordinate and a y co-ordinate . When plotting a graph, we are interested in ALL those points whose co-ordinates satisfy some rule or other. For example, consider ALL those points whose co-ordinates add up to 8. x y 0 8 1 7 2 6 3 5 etc. There are billions of such points! x + y = 8 ALWAYS label the graph! x y

3. y = x y = 2x y = 3x y = ½x x y 0  0 3  3 -4  -4 x y 0  0 3  6 -4  -8 x y 0  0 2  6 -3  -9 x y 0  0 8  4 4  2 Example 1. We will plot 4 graphs on a single set of axes. x y

4. y = x + 2 y = x - 4 y = 2x - 3 y = 3x - 5 x y 0  2 1  3 2  4 x y 0  -4 1  -3 2  -2 x y 0  -3 1  -1 2  1 x y 0  -5 1  -2 2  1 Example 2. x y

5. Y = 8 Y = 4 Y = 2 Y = 0 Y = -3 Y = -8 Lines parallel to the y axis x = 9 x = 0 x = 5 x = - 4 x = - 7 0 1 2 3 4 5 6 7 8 9 10 -9 -8 -7 -6 -5 -4 -3 -2 -1 -10 x y 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 -8 -9 -10 Lines parallel to the x axis

6. Question 1. Plot the following 4 graphs on a single set of axes. a) y = x b) y = x + 3 c) y = x + 6 d) y = x  4 x y

7. Question 2. Plot the following 4 graphs on a single set of axes. a) y = 2 x b) y = 2 x + 3 c) y = 2 x  1 d) y = 2 x  3 x y

8. Question 3. Plot the following 3 graphs on a single set of axes. a) y = 10  x b) y = 8  x c) y = 4  x x y

9. Question 4. Plot the following 3 graphs on a single set of axes. a) y = 3 x b) y = 3 x  3 c) y = 3 x + 4 x y

10. Question 5. Plot the following 4 graphs on a single set of axes. a) x + y = 9 b) x + y = 6 c) x + y = 3 d) x + y = 0 x y

11. Question 6. Plot the following 3 graphs on a single set of axes. a) y = 10  2 x b) y = 6  2 x c) y = 9  3 x x y

12. Question 7. Plot the following 3 graphs on a single set of axes. a) y = 8  x b) y = 8  2 x c) y = 8  4 x x y