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 = 
.
As the speed is constant, we get
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
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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