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To determine the missing value \( a \) that makes the table represent a linear function, we need to ensure that the rate of change between \( x \) and \( y \) is constant.

From the given values:
- When \( x = 2 \), \( y = 2.80 \)
- When \( x = 4 \), \( y = 5.60 \)

First, calculate the rate of change between these points:
\[
\text{Slope} = \frac{5.60 - 2.80}{4 - 2} = \frac{2.80}{2} = 1.40
\]

The slope tells us that for each increase of 1 in \( x \), \( y \) increases by 1.40. We can use this to find \( a \), the cost when \( x = 3 \):
\[
y = y_1 + \text{slope} \times (x - x_1)
\]
\[
a = 2.80 + 1.40 \times (3 - 2) = 2.80 + 1.40 = 4.20
\]

So, the missing value \( a \) that makes the table represent a linear function is \( \textbf{4.20} \).

Would you like to know more details about how this calculation is performed, or do you have any other questions?

**Relative Questions:**
1. How would you calculate the y-intercept of this linear function?
2. What would the cost be for 5 pounds, using the same linear function?
3. Can you explain why the relationship between pounds and cost is linear?
4. What is the general formula for a linear function and how can you derive it from two points?
5. How do changes in the slope affect the graph of a linear function?

**Tip:** When you have two points from a linear relationship, you can always find the slope by dividing the change in y by the change in x. This slope is constant across the graph of the function.

What is the missing value, a, that makes the table represent a linear function?

Learn how to determine the missing value that makes the table represent a linear function. This problem involves key concepts such as calculating the slope and using linear equations to solve for unknowns. Suitable for Grades 6-8 students.

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