1. Starter: A)y = x + 1 B) y = x – 1

2. Real Life Graphs Objective: To understand how graphs are used to show relationships between variables Must: Read table accurately Could: Interpret graphs Should: Draw conclusion from Velocity graphs

3. Plotting graphs – using a table of values When we plot a graph we usually start with a table of values. The values in the table usually come from a formula or equation or from an observation or experiment. For example, a car hire company charges £30 to hire a car and then £25 for each day that the car is hired. This would give us the following table of values: The cost of the car hire depends on the number of days. The number of days must therefore go in the top row. Number of days, d Cost in £, c 12345 5580105130155

4. Plotting graphs – choosing a scale The next step is to choose a suitable scale for the axes. Look at the values that we need to plot. Number of days, d Cost in £, c 12345 5580105130155 The number of days will go along the horizontal axis. The numbers range from 1 to 5. A suitable scale would be 2 units for each day. The cost will go along the vertical axis. The cost ranges from 55 to 155. A suitable scale would be 1 unit for each £10. We could start the scale at £30.

5. Plotting graphs – drawing the axes We then have to draw the axes using our chosen scale. We will need at least 10 squares for the horizontal axis and 13 squares for the vertical axis. When the scale does not start at 0 we must show this with a zigzag at the start of the axis. Number the axes. 30 40 50 60 70 80 90 100 110 120 130 140 150 012345 Label the axes, remembering to include units, if necessary. Number of days Cost (£)

6. Plotting graphs – plotting the points Use the table of values to plot the points on the graph. Number of days, d Cost in £, c 12345 5580105130155 0 0 30 40 50 60 70 80 90 100 110 120 130 140 150 12345 Number of days Cost (£) It is most accurate to use a small cross for each point. If appropriate, join the points together using a ruler. Lastly, don’t forget to give the graph a title. Cost of car hire

7. Science experiment Mass of object moving down ramp (grams) Time taken for object to move down ramp (seconds) 100 4 150 7 200 12 250 17 A group of pupils are doing an experiment to explore the effect of friction on an object moving down a ramp. They attach weights of different mass to the object and time how long the object takes to reach the bottom of the ramp. They put their results in a table and use the table to plot a graph of their results.

8. Science experiment Mass of object moving down ramp (grams) Time taken for object to move down ramp (seconds) 100 4 150 7 200 12 250 17 Mass of object (grams) 0 4 8 12 16 20 050100150200250300 Time taken (seconds) We can join the points using straight lines. Do the intermediate points have any practical significance? How could we make the graph more accurate?

9. Travel Graphs A travel graph gives information about how someone or something has travelled over a given time period. It is also called a distance–time graph. You can find the average speed from a distance–time graph by using the formula: average speed = total distance travelled total time taken You always work out the distance travelled in 1 hour to get the speed in kilometres per hour (km/h) or miles per hour (mph).

10. Distance-time graphs In a distance-time graph the horizontal axis shows time and the vertical axis shows distance. For example, John takes his car to visit a friend. There are three parts to the journey: John drives at constant speed for 30 minutes until he reaches his friend’s house 20 miles away. He stays at his friend’s house for 45 minutes. He then drives home at a constant speed and arrives 45 minutes later. 0 time (mins) distance (miles) 153045607590105120 5 10 15 20 0