Question

Which of the following equations represents the graph shown?

Answer 1

Answer:
`f(x)=(3)/(2)x`.

Explanation:

Assume one block in the graph takes one value.

From the given graph, it can be seen that the line is passing through two points (0,0) and (2,3).

We know that the equation of a line passing through points (a,b) and (c,d) is given by :-

`(y-b)=(d-b)/(c-a)(x-a)`

Then , the equation of a line passing through points (0,0) and (2,3) is given by :-

`(y-0)=(3-0)/(2-0)(x-0)\\\\\Rightarrow y=(3)/(2)x`

Hence, the equations represents the given graph
`f(x)=(3)/(2)x`.

Answer 2

`y=(3)/(2)x`

Explanation:

The given line passes through the origin.

Its equation is of the form;

`y=mx`

where

`m=(3)/(2)` is the slope of the line.

The required equation is

`y=(3)/(2)x`