Question

Enter the correct answer in the box.
An airport has two long-term parking lots. The cost to park, y, in each lot for x days is shown in the tables.

Lot A
Days Parked Cost
1 $16
2 $20
3 $24
4 $28
Lot B
Days Parked Cost
1 $6
2 $12
3 $18
4 $24

A system of linear equations can be used to determine on which day the cost to park is the same for both lots. One of the equations in the system is y = 6x. What is the other equation in the system?

Answer 1

To find the other equation in the system, we will determine the relationship between the number of days parked \(x\) and the cost \(y\) for Lot A based on the information given.

Looking at Lot A's cost data:
- For 1 day, the cost is $16
- For 2 days, the cost is $20
- For 3 days, the cost is $24
- For 4 days, the cost is $28

From this, we can observe that the cost for Lot A increases by $4 for each additional day parked. This indicates that Lot A follows a linear relationship.

Let’s write the equation for Lot A. We notice that it can be expressed as:

- The cost for 1 day is $16, so we can express the cost in terms of days parked as:

\[
y = mx + b
\]

Where:
- \(m\) is the slope (rate of change per day)
- \(b\) is the y-intercept (the cost when \(x = 0\))

We can calculate \(m\) (slope) for Lot A:
The rise (change in cost) per day could be derived from \(16\) to \(20\) which is \(20 - 16 = 4\).
So, \(m = 4\).

To find the y-intercept, we can plug in a point. If we let \(x = 1\) (for 1 day):
\[
16 = 4(1) + b \\
b = 16 - 4 \\
b = 12
\]

Thus, the equation of Lot A becomes:
\[
y = 4x + 12
\]

So, the system of equations is:
1. \(y = 6x\) (for Lot B)
2. \(y = 4x + 12\) (for Lot A)

Therefore, the other equation in the system is:
\[
y = 4x + 12
\]