Question

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

• A. $\$3$ million per year
  
• B. $\$1$ million per year
  
• C. $\$2$ million per year
  
• D. $\$4$ million per year
  

Answer 1

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 $=\frac{\text{rise}}{\text{run}}=\frac{\text{change in}y}{\text{change in}x}=\frac{y_2-y_1}{x_2-x_1}=\frac{4-2}{2-1}=\$2$ 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.