Question

# Is the relation forms a linear function ?

Use the graph to support your answer.

Hint:

### An equation of the form y = f(x) is called a function if there is a unique value of y for every value of x. In other words, every value of x must have one value of y. We can check if the graph is a function by the vertical line test. A graph represents a function if any vertical line in the xy plane cuts the graph at maximum one point. A function is linear if the graph of the function is a straight line.

## The correct answer is: function is linear

*Step by step solution:*

Let us denote the week by x.

Let us denote the number of students by y.

The given table is

x

0

1

2

3

4

5

y

300

250

200

150

100

50

We draw a graph from the above table.

From the graph, we can observe that, the curve 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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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.