Select all the correct answers.
The table shows the average bill totals for given numbers of diners at Simone’s restaurant. If the rate is constant and you graph this relationship with the number of people along the x-axis and bill amounts along the y-axis, which points will lie on the line you get?

Persons	Bill Amount
1
$40
2
$80
7
$280
9
$360
11
$440
 (12, 460)
 (20, 800)
 (24, 1,020)
 (27, 1,080)
 (28, 1,110)

Given that the relationship between the number of persons and the bill amount is linear and constant, we first need to find the rate. By observing the dataGiven that the relationship between the number of persons and the bill amount is linear and constant, we first need to find the rate. By observing the 

\[
\text{Rate per person} = \frac{\text{Bill Amount}}{\text{Number of Persons}} = \frac{40}{1} = 40 \, \text{dollars per person}
\]

Now we check which of the given points (persons, bill amount) will lie on the line.

\[
\text{Bill Amount} = \text{Number of Persons} \times 40
\]

### Check the given points:

1. (12, 460)
   \[
   12 \times 40 = 480 \quad (\text{not } 460)
   \]
   This point does not lie on the line.

2. (20, 800)
   \[
   20 \times 40 = 800
   \]
   This point lies on the line.

3. (24, 1,020)
   \[
   24 \times 40 = 960 \quad (\text{not } 1,020)
   \]
   This point does not lie on the line.

4. (27, 1,080)
   \[
   27 \times 40 = 1,080
   \]
   This point lies on the line.

5. (28, 1,110)
   \[
   28 \times 40 = 1,120 \quad (\text{not } 1,110)
   \]
   This point does not lie on the line.

### Correct Points:

- (20, 800)
- (27, 1,080)

Therefore, the correct answers are:

- (20, 800)
- (27, 1,080)

Do you want details or have any questions?

Here are 5 questions you can ask next:
1. How do you determine if a point lies on a line given its equation?
2. What is the slope of the line representing the relationship between the number of persons and the bill amount?
3. How can you use a table of values to create a graph?
4. What are the characteristics of a linear relationship in a graph?
5. How do you interpret the slope and y-intercept in the context of this problem?

**Tip:** When verifying points on a linear graph, multiply the x-coordinate by the constant rate and check if it matches the y-coordinate.

Learn how to determine which points lie on a linear graph representing the relationship between the number of persons and the bill amount. This problem involves finding the rate of change, graphing linear relationships, and checking points on a line. Suitable for students in Grades 9-10.

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