The problem asks you to write an equation for the revenue of a company, given:

• The revenue has been increasing at a steady rate of $45,000 per year since 2000.
• In 2000, the company's revenue was $2,900,000.

Slope-Intercept Form:

We use the slope-intercept form of a linear equation: $y = mx + b$ Where:

• $m$ is the slope (the rate of change, which is $45,000 per year),
• $b$ is the y-intercept (the revenue at $x = 0$, which corresponds to the year 2000).

Step-by-Step:

1. Slope (Rate of Change): The revenue increases by $45,000 per year, so $m = 45,000$.

2. Y-Intercept (Initial Value): The revenue in 2000 was $2,900,000, so $b = 2,900,000$.

Therefore, the equation is: $y = 45,000x + 2,900,000$ Where:

• $y$ is the company's revenue after $x$ years since 2000.
• $x$ is the number of years since 2000.

Final Equation:

$y = 45,000x + 2,900,000$

Would you like any further details on how this equation models the company's revenue, or do you have any other questions?

Here are some related questions for further practice:

1. How can you use this equation to predict the company's revenue in 2025?
2. What would happen to the equation if the growth rate changed after 2010?
3. How would you modify this equation to include a situation where revenue decreases?
4. How do you interpret the slope and y-intercept in a business context?
5. How could this model be visualized graphically?

Tip: Always ensure units are consistent, especially when dealing with large values like revenues!