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?(1 point)

Question

Responses

y=10,000x−2,760,065
𝑦
=
10
,
000
𝑥
−
2
,
760
,
065
y is equal to 10 comma 000 x minus 2 comma 760 comma 065

y=10,000x+2,760,065
𝑦
=
10
,
000
𝑥
+
2
,
760
,
065
y is equal to 10 comma 000 x plus 2 comma 760 comma 065

y=2,760,065x+10,000
𝑦
=
2
,
760
,
065
𝑥
+
10
,
000
y is equal to 2 comma 760 comma 065 x plus 10 comma 000

y=−10,000x+2,760,065

Answer 1

To find the equation of the line that represents the total population \( y \) in terms of years \( x \), we start with the current population and the rate of increase.

1. Current Population: The population is currently 2,760,065, which we can denote as \( y_0 = 2,760,065 \).
2. Rate of Increase: The population is increasing by 10,000 people per year. This translates to a slope (rate of change) of \( 10,000 \).

The equation of a line can be represented in the slope-intercept form \( y = mx + b \), where:

• \( m \) is the slope (rate of growth).
• \( b \) is the y-intercept (initial population).

Here, after \( x \) years, the population \( y \) will be:

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

Where:

• \( 10,000x \) represents the increase in population after \( x \) years.
• \( 2,760,065 \) is the current population when \( x = 0 \).

Thus, the correct equation of the line representing the total population \( y \) in terms of years \( x \) is:

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

So the correct response is:

y = 10,000x + 2,760,065.