Maths-
General
Easy

Question

# A train leaves the station at time . Travelling at a constant speed, the train travels 360 kilometers in 3 hours. a) Write a function that relates the distance travelled ,d to the time, . b) Graph the function and tell whether it is a linear function or non linear function.

Hint:

## The correct answer is: 120t

### Step by step solution:Let us denote the time taken by the train by t.Let us denote the distance travelled by d.Given,Distance travelled by the train =360 kmTime taken to travel the above distance = 3 hoursWe know, speed = .As the speed is constant, we getThus, the constant speed of the train is 120 km per hour.Finally, we get,The train travels a distance d in time t at speed 120 km per hour.So, the relation between t and d is given byThus, a function that relates the distance travelled by the train in time t isd = 120tTo graph the function, first we make a table of different values of x and the corresponding values of y. t 0 1 2 3 4 5 d 0 120 240 360 480 600 Now, we plot these points in the graph.From the graph it can be seen that the line drawn is a straight line. Hence, the function is linear.

There are other ways to determine whether a function is linear or not, like, checking if the slope is equal between each of the points or if the equation can be written in the form of y = ax + b, where a and b are constants.