Question

The graph below represents a nonlinear function. Which of the following movements of a point $B$ will make the function a linear one?

Answer 1

Let us consider each option to check in which case movement of the point will make the function from point $A$ to $D$, a linear one.
We will consider one by one option to change the position of point $B$ and we will observe the graph of the new function.
We know the representation of a linear function on the graph is a straight line.

Point $Q$ will be moved to $(-40,60)$:The given graph is not a straight line.
And as the graphical representation of any linear function is a straight line, so it is not a linear function.

Point $Q$ will be moved to $(-20,40)$:

The given graph is not a straight line.
And as the graphical representation of any linear function is a straight line, so it is not a linear function.

Point $Q$ will be moved to $(-10,10)$:
The given graph is not a straight line.
And as the graphical representation of any linear function is a straight line, so it is not a linear function.

Point $B$ will be moved to $(-30,70)$:

The given graph is a straight line.
And as the graphical representation of any linear function is a straight line, so it is a linear function.

So option D is the correct answer.