The given graph shows the revenue of a company in million dollars $(y)$ for a given number of years $(x)$ . What is the growth rate of the company over the years?

$ 3

million per year

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$ 1

million per year

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$ 2

million per year

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$ 4

million per year

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Solution

The correct option is C $$ 2$ million per year

Let’s consider two points on the graph, $(1, 2)$ and $(2, 4)$ .

We can write, $(x_{1}, y_{1}) = (1, 2)$ and $(x_{2}, y_{2}) = (2, 4)$ .
Here, the growth rate of the company can be calculated by finding the slope of the graph, i.e.,
Growth rate = slope of the line $= \frac{rise}{run} = \frac{change in y}{change in x} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{4 - 2}{2 - 1} = $ 2$ million per year

Alternate solution:
On a graph of a proportional relationship, point $(1, k)$ represents the unit rate, $k : 1$ , and the constant of proportionality, $k$ .
So, from the point $(1, 2)$ , the unit rate which is the growth rate here is determined as $$ 2$ million per year.

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The given graph shows the revenue of a company in million dollars (y) for a given number of years (x). What is the growth rate of the company over the years?

The given graph shows the revenue of a company in million dollars $(y)$ for a given number of years $(x)$ . What is the growth rate of the company over the years?