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:

First, we find the constant speed of the train. Then we derive a function representing the relation between distance travelled and time taken by the train. Further, we make a table of different values of d for different values of t. Then we make a graph representing the equation. Recall that a function is said to be linear if the graph of the function in the xy plane is a straight line.

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 km
    Time taken to travel the above distance = 3 hours
    We know, speed = fraction numerator text  distance  end text over denominator text  time  end text end fraction.
    As the speed is constant, we get
    text  speed  end text equals 360 over 3 equals 120
    Thus, 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 by
    120 equals d over t
    Thus, a function that relates the distance travelled by the train in time t is
    d = 120t
    To 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.

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