Question

Sketch a graph between the production and time taken for the production from the following table:

Time (in days)	Production (in thousands)
2	4
6	12
9	18

Select the correct option regarding the nature of the graph obtained.

• A. The graph is a non-linear one
• B. The graph is a linear one
• C. The graph has slope = 0
• D. None of the above

Answer 1

The correct option is B The graph is a linear one

Time (in days)	Production (in thousands)
2	4
6	12
9	18

$\text{We know, Slope}=\frac{\text{Change in y}}{\text{Change in x}}$

Plottiong the points (2,4), (6,12), and (9,18) on the graph, we get:


A graph is said to be linear, if it has a constant slope.

As the production is in thousands, we have to multiply y-value with 1000.

Calculating the slope for (2,4000) and (6,12000), we get:

$\text{Slope}=\frac{\text{Change in y}}{\text{Change in x}}=\frac{12000-4000}{6-2}=2000$

Calculating the slope for (6,12000) and (9,18000), we get:

$\text{Slope}=\frac{\text{Change in y}}{\text{Change in x}}=\frac{18000-12000}{9-6}=2000$

Hence, the slope of the function is constant.

Therefore, the graph is linear.