Select all the correct answers.
The table shows the balance of Steven's savings account over time. Assuming there are no withdrawals, if you graph the relationship for Steven's monthly balances, which points will lie on the resulting line?

Month	Balance
1	$400
3	$1,200
7	$2,800
9	$3,600
13	$5,200
 (22, 8,400)
 (23, 9,200)
 (24, 8,800)
 (26, 10,400)
 (27, 10,600)


To determine which points will lie on the resulting line representing Steven's savings account balance over time, we need to find the linear relationship between the month and the balance. We can do this by calculating the slope and the y-intercept from the given data points and then checking if the other points fit this linear equation.

First, let's find the slope (m) of the line. We'll use the points (1, 400) and (3, 1200):

\[ m = \frac{1200 - 400}{3 - 1} = \frac{800}{2} = 400 \]

Now that we know the slope is $400 per month, we can find the y-intercept (b) using the point (1, 400):

\[ 400 = 400(1) + b \]
\[ b = 400 - 400 \]
\[ b = 0 \]

The equation of the line is:

\[ \text{Balance} = 400 \times \text{Month} \]

Now, we need to check if the points (22, 8400), (23, 9200), (24, 8800), (26, 10400), and (27, 10600) lie on this line:

1. For (22, 8400):
\[ 400 \times 22 = 8800 \]
\[ 8400 \neq 8800 \]

2. For (23, 9200):
\[ 400 \times 23 = 9200 \]
\[ 9200 = 9200 \]

3. For (24, 8800):
\[ 400 \times 24 = 9600 \]
\[ 8800 \neq 9600 \]

4. For (26, 10400):
\[ 400 \times 26 = 10400 \]
\[ 10400 = 10400 \]

5. For (27, 10600):
\[ 400 \times 27 = 10800 \]
\[ 10600 \neq 10800 \]

Therefore, the points (23, 9200) and (26, 10400) will lie on the resulting line.

Would you like more details or have any questions about this?

Here are 5 numbered questions you can ask:
1. How do you find the slope of a line from a table of values?
2. What is the process for finding the y-intercept of a linear equation?
3. How do you graph a linear equation on a coordinate plane?
4. How can you check if a point lies on a given line?
5. What are the applications of linear equations in real life?

Tip: To verify if a point lies on a line, substitute the point's coordinates into the line's equation and see if the equation holds true.

Explore the relationship between time and Steven's savings account balance through graphing. Understand how to determine the linear equation representing the balance over months and verify which data points lie on this line.

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