Which graph correctly represents the relationship between arc length and the measure of the corresponding central angle on a circle with radius r?

Please note that the options for the graphs are missing in the question posted. However, I will try my best to answer the question as there is just one graph that is possible.

Please find the two attached diagrams to get a better understanding of the answer provided here.

Let us consider the first diagram. Here, we have a circle with center O. The radius of the circle is . Let the length of the arc be and it subtends an angle at the centre.

Now, we know that the relationship between arc length, , radius, and angle subtended is given as:

Thus, the relationship is linear and the graph between and for a given will be a straight line whose slope will be given by .

Now, we also know that the maximum arc length that a circle can possibly have is the circumference of the circle which is given by and that happens when the angle subtended at the center is equal to .

Keeping the information of the above two paragraphs please have a look at the second diagram.

This second diagram is the required graph as asked in the question.