Graph Period 1-2
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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.
Graph Period 1-2
- 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