Linear Relationships

Review -Linear or Not? A = 100 + 60t Time (sec) 1 2 3 Volume 600 300 1 2 3 Volume 600 300 150 75 Water is leaking out of a water tank, such that the amount of water remaining in the tank is given by the formula V = 3000 – 50t, where V is the volume of water in the tank in litres and t is the time it takes to drain (in minutes). Time 4 8 12 Distance 30 430 830 1230

Gradient What does the gradient of a line mean? How can you find the gradient from any situation? How can you find the gradient if given a graph, table or rule? What is the difference between positive and negative gradient? What is the difference

What is the rate of change (gradient) of water per minute? What is the vertical intercept and what does this mean in this situation?

Gradient

Hannah’s driving trip Some friends are on a car trip from Brisbane to Sydney. After 200 km, Hannah takes over the driving and drives the rest of the way. Brisbane is 920 km from Sydney. Every 2 hours Hannah has driven another 160 km.   a) Complete these coordinates for (t, d) where t is the time that Hannah has been driving and d is the total distance from Brisbane. (0, 200) (2, __) (4, __) (6, __) (8, __) b) Name the independent variable and the dependent variable. c) Graph using an appropriate axes d) What is the vertical axis intercept? What does it mean in this situation? e) What is the rate of change (gradient) of this line? What does it mean in this situation? f) Write a rule relating t and d

Practice Ex. 9B.2 p199 Q1,3,4