General Mathematics · Unit 1 · Linear equations and their graphs · Straight-line graphs
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A mobile phone plan charges a monthly base fee plus a rate per gigabyte (GB) of data used. The total monthly cost, \(C\) dollars, is modelled by the linear function \(C = 18 + 6d\), where \(d\) is the number of gigabytes of data used. Which statement correctly interprets the gradient of this function?
A car rental company tracks the relationship between the number of days \(d\) a customer rents a vehicle and the total cost \(C\) in dollars. The company models this relationship using the linear function \(C = 45d + 120\). (a) Interpret the slope of this linear model in the context of car rental costs. (1 mark) (b) Interpret the \(y\)-intercept of this linear model in the context of car rental costs. (1 mark) (c) Use the model to calculate the total cost for a customer who rents the vehicle for 7 days. (1 mark)
A transport logistics company analysed the relationship between the number of delivery trucks in operation and their weekly fuel costs. The data was collected over 8 weeks and a least-squares regression line was fitted, where y represents the total weekly fuel cost (in dollars) and x represents the number of trucks in operation. The regression equation is: y = 385x + 1240 (a) Interpret the slope of the fitted line in the context of this situation. (2 marks) (b) Interpret the y-intercept of the fitted line in the context of this situation. (2 marks)