The population of a city is currently 2,760,065. The population is increasing at a rate of 10,000 people per year. Which is the equation of the line that represents the total population, y, in terms of years, x?

Answer 1

To represent the total population \( y \) in terms of years \( x \), we can use the following linear equation:

\[ y = mx + b \]

where:

• \( m \) is the rate of increase (the slope), which is \( 10,000 \) people per year,
• \( b \) is the current population, which is \( 2,760,065 \).

Since we are starting from the current population and looking at the increase over the years, we can express this as follows:

\[ y = 10,000x + 2,760,065 \]

In this equation:

• \( y \) is the total population after \( x \) years,
• \( 10,000x \) represents the increase in population after \( x \) years,
• \( 2,760,065 \) is the initial population.

Thus, the equation of the line that represents the total population is:

\[ y = 10,000x + 2,760,065 \]