Let's analyze the given information and solve the problems step-by-step.

The linear equation provided is: $y = 291.4x + 2944.02$ where:

• $y$ represents the total cost,
• $x$ is the number of years after 2000.

(a) Find and interpret the slope of this equation.

In a linear equation of the form $y = mx + b$:

• $m$ represents the slope.
• $b$ represents the y-intercept.

Here, the slope $m = 291.4$.

Interpretation of the slope: The slope of $291.4$ indicates the yearly increase in the cost of tuition and fees. This means that each year, the cost increases by approximately $291.4.

So, the correct answer is:

• A. The slope (291.4) indicates an increase in yearly cost.

(b) Find and interpret the y-intercept of this equation.

The y-intercept $b = 2944.02$.

Interpretation of the y-intercept: The y-intercept represents the estimated cost of tuition and fees in the year 2000 (when $x = 0$). Therefore, the y-intercept of 2944.02 suggests that in the year 2000, the cost was approximately $2944.02.

Would you like further details or have any questions on these interpretations?

Here are five related questions to deepen your understanding:

1. How would the interpretation change if the slope were negative?
2. What would the estimated cost be in 2010 using this model?
3. How would you adjust this model if you knew the costs were expected to increase more rapidly in the future?
4. How can this equation help in budgeting for future college expenses?
5. What factors could cause deviations from this linear trend in real tuition costs?

Tip: In linear functions, the slope shows the rate of change, while the y-intercept provides a starting point or initial value when $x = 0$.