Direct Proportionality and Graphs

1
Direct Proportionality and Graphs
2
Direct proportionality

• x and y are always in the same ratio
• as one quantity doubles, trebles etc., so does
  the other
• y ? x
• y kx

3
Direct proportionality

• y kx
• straight line
• through (0,0)
• Where does k appear on the graph?
• You can use the graph to read off other values

4
Proportionality graphs(1)

• Lizzie is in the park at 12 noon. She measures
  the length of her shadow as 2m. She knows that
  her actual height is 1.6m.
• Draw a graph to illustrate the relationship
  between height and shadow length at 12 noon.
• What is the length of shadow of a tree which is
  4m high?
• What is the actual height of a bush which casts a
  shadow 1.25m long?
• Use your graph to find the constant of
  proportionality and write down the equation of
  the graph.

5
Proportionality graphs (2)

• A deep-sea diver thinks that the pressure of
  water at different depths is directly
  proportional to the depth of water.
• In an experiment he records the data given below.
  Draw a graph and use it to answer these
  questions
• Was the diver right?
• What is the gradient of your graph?
• Write down a formula connecting depth and
  pressure
• Predict the pressure at a depth of 6m.