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.