Question

The given graph shows the relation between time and number of downloads of two songs.


represent(s) a linear graph.

• A. None of the graph
• B. Graph of Song 1
• C. Both of the graphs
• D. Graph of Song 2

Answer 1

The correct option is D Graph of Song 2

For Song 1:

From the graph, we observe:


Consider any two points, say (0,2) and (1,4)

$\text{Slope}=\frac{\text{Change in y}}{\text{Change in x}}=\frac{4\times 1000-2\times 1000}{1-0}$

$\left[\text{Multiply "y" values with 1000 as "y" is given in}\right]$ $\left[\text{thousands}\right]$

$\therefore \text{Slope = 2000}$

Consider other two points, (1,4) and (2,4).

$\text{Slope}=\frac{\text{Change in y}}{\text{Change in x}}=\frac{4\times 1000-4\times 1000}{2-1}$

$\therefore \text{Slope = 0}$

Slope of the graph varies, hence it is not a linear function.

For Song 2:

From the graph, we observe​​​​​:


Consider any two points, say (2,0) and (3,2)

$\text{Slope}=\frac{\text{Change in y}}{\text{Change in x}}=\frac{2\times 1000-0\times 1000}{3-2}$

$\left[\text{Multiply "y" values with 1000 as "y" is given in}\right]$ $\left[\text{thousands}\right]$

$\therefore \text{Slope = 2000}$

As, it is straight line, slope remains constant.

Hence, it is a linear function.