Choose the correct statement representing the unit rates of the two companies as shown in the graph.

Unit Rate of Company 1 > Unit Rate of Company 2

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Unit Rate of Company 1 < Unit Rate of Company 2

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Unit Rate of Company 1 = Unit Rate of Company 2

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Cannot be determined

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Solution

The correct option is B Unit Rate of Company 1 < Unit Rate of Company 2
You know,
$U n i t r a t e = \frac{c h a n g e i n y}{c h a n g e i n x} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Company 1:

Consider the points (2, 3) and (4, 6)
∴ Unit rate of company 1 =
$\frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{6 - 3}{4 - 2} = 1.5$

Company 2:

Consider the points (1, 2.5) and (3, 7.5)
∴ Unit rate of company 2 =
$\frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{7.5 - 2.5}{3 - 1} = 2.5$

So,
Unit rate of company 1 < Unit Rate of company 2

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