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.

### Related Questions to study

### Do the ordered pairs plotted in the graph below represents a function? Explain.

In a function, every value of x must have one value of y. When we draw a vertical, it cuts x axis at one point, we take that point to be x. If the vertical line cuts the graph at two points, then it gives two values of y for one value of x. This does not represent a function.

### Do the ordered pairs plotted in the graph below represents a function? Explain.

In a function, every value of x must have one value of y. When we draw a vertical, it cuts x axis at one point, we take that point to be x. If the vertical line cuts the graph at two points, then it gives two values of y for one value of x. This does not represent a function.

### The relationship between the number of hexagons, , and the perimeter of the figure they form, , shown in the graph. Is the perimeter of the figure a function of the number of hexagons? Explain.

In a function, every value of x must have one value of y. When we draw a vertical, it cuts x axis at one point, we take that point to be x. If the vertical line cuts the graph at two points, then it gives two values of y for one value of x. This does not represent a function.