Question

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)
$y = -10,000x + 2,760,065$
$y = 10,000x + 2,760,065$
$y = 2,760,065x + 10,000$
$y = 10,000x - 2,760,065$
graphing calculator

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a linear equation is $y = mx + b$, where $m$ is the slope (rate of change) and $b$ is the y - intercept (initial value).

Step2: Identify $m$ and $b$

• The initial population (when $x = 0$, i.e., at the start) is $2760065$. So, $b=2760065$.
• The population is increasing at a rate of $10000$ people per year. The rate of change (slope) $m = 10000$ (since the population is increasing, the slope is positive).

Step3: Form the equation

Substitute $m = 10000$ and $b = 2760065$ into the slope - intercept form $y=mx + b$. We get $y=10000x + 2760065$.

Answer:

$\boldsymbol{y = 10,000x + 2,760,065}$ (the second option)