Find the function that relates the two variables and graph the function.

Question

The instrument reported back that the number of cars passing each minute varied linearly between 6.30am and 8.30am. The instrument reported 55 cars passing in 1 minute at 7.00am while at 8.00am, 115 cars passed in 1 minute. Fully communicate your working to do the following.

Answer 1

First work out the gradient. If t represents the time in minutes after 6.30am and c the number of cars passing per minute, then the gradient is (difference in numbers of cars)/(difference in time)=(115-55)/(90-30) because t=30 at 7.00am and t=90 at 8.00am. So the gradient is 60/60=1. We can now write c=t+A where we need to find the constant A. When t=30, c=55 so 55=30+A, making A=25. The linear equation is c=t+25.