To address the problem:

Step 1: Analyze the graph

The graph plots the number of chocolates $C$ remaining in the box against the number of days $t$ after Liam's birthday. The line on the graph is linear and decreasing.

Step 2: Determine the equation of the line

The general equation of a line is: $C = mt + b$ where:

• $m$ is the slope,
• $b$ is the y-intercept.

From the graph:

• The y-intercept ($b$) is 28, as the graph starts at 28 chocolates when $t = 0$.
• The slope ($m$) can be calculated using two points from the line:
  • Point 1: $(0, 28)$
  • Point 2: $(10, 0)$

The slope formula is: $m = \frac{\Delta C}{\Delta t} = \frac{C_2 - C_1}{t_2 - t_1}$ Substitute the points: $m = \frac{0 - 28}{10 - 0} = -\frac{28}{10} = -2.8$

Thus, the equation is: $C = -2.8t + 28$

Step 3: Interpretation of the slope

The slope is $-2.8$, which means that Liam eats 2.8 chocolates per day on average. In context:

• Negative slope: The number of chocolates decreases daily.
• Magnitude: Liam eats 2.8 chocolates per day.

Final Answer

1. Equation: $C = -2.8t + 28$
2. Slope: $-2.8$
3. Interpretation: Liam eats 2.8 chocolates per day, reducing the total number of chocolates in the box daily.

Let me know if you need further clarification!

Here are some related questions:

1. What would be the equation if Liam started with 40 chocolates instead of 28?
2. How many days would it take for Liam to finish the chocolates completely?
3. How does the graph change if Liam eats more chocolates per day?
4. What is the meaning of the y-intercept in this problem?
5. Can this function $C = -2.8t + 28$ take non-integer values for $t$? Why or why not?

Tip: Always double-check the slope by selecting different points if unsure of the graph's increments.