Construct and analyse a straight-line graph to model a given linear relationship, e.g. modelling the cost of filling a fuel tank of a car against the number of litres of petrol required.

A plumber charges a call-out fee of $\$65$ plus $\$40$ per hour of labour. Which graph correctly represents the relationship between the total cost (in dollars) and the hours of labour worked?

A gym charges a membership fee plus a charge per visit. The relationship between the number of visits and total cost is linear. After 5 visits, the total cost is \$75. After 12 visits, the total cost is \$138. (a) Find the charge per visit. [1] (b) Find the membership fee. [1] (c) Write the equation of the line that models the total cost (in dollars) as a function of the number of visits. [1]

A solar panel installation company charges a fixed call-out fee plus a cost per square metre of panel installed. (a) Construct a straight-line graph to display the relationship between area of panels installed and total cost on the grid provided. (3 marks) (b) Use your graph to determine the cost of installing \(45\) square metres of panels. (1 mark) (c) Calculate the gradient of the line and interpret its meaning in the context of this situation. (1 mark)