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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
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B
The graph is a linear one
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C
The graph has slope = 0
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D
None of the above
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Solution

The correct option is B The graph is a linear one
Time (in days) Production (in thousands)
2 4
6 12
9 18

We know, Slope=Change in yChange 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:

Slope=Change in yChange in x=12000 40006 2=2000

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

Slope=Change in yChange in x=18000 120009 6=2000

Hence, the slope of the function is constant.

Therefore, the graph is linear.

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