Question

example 6
the number of online shoppers in the united states can be modeled by the equation y = 5.88x + 172.3, where y represents the number of millions of online shoppers in the united states x years after 2010. estimate the number of online shoppers in 2020.
the y - intercept is , which means that there were million online shoppers in 2010.
the slope is which means that the number of online shoppers increased at a rate of million people per year.
in 2020, there were approximately million online shoppers in the united states.
online shoppers in the united states
graph with x - axis labeled years after 2010 (0 - 10) and y - axis labeled number of shoppers (millions) (0 - 250)

Explanation:

Step1: Identify y - intercept

The equation of the line is in the form $y = mx + b$, where $b$ is the y - intercept. For $y = 5.88x+172.3$, the y - intercept $b = 172.3$. This means there were 172.3 million online shoppers in 2010.

Step2: Identify slope

In the equation $y = 5.88x + 172.3$, the coefficient of $x$ is the slope $m$. So the slope $m = 5.88$, which means the number of online shoppers increased at a rate of 5.88 million people per year.

Step3: Calculate x for 2020

The year 2020 is $2020 - 2010=10$ years after 2010, so $x = 10$.

Step4: Find number of shoppers in 2020

Substitute $x = 10$ into the equation $y = 5.88x+172.3$. Then $y=5.88\times10 + 172.3=58.8+172.3 = 231.1$.

Answer:

The y - intercept is 172.3, which means that there were 172.3 million online shoppers in 2010.
The slope is 5.88 which means that the number of online shoppers increased at a rate of 5.88 million people per year.
In 2020, there were approximately 231.1 million online shoppers in the United States.