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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 Balance1 $4003 $1,2007 $2,8009 $3,60013 $5,200 (22, 8,400) (23, 9,200) (24, 8,800) (26, 10,400) (27, 10,600)

Question

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 Balance1 40034003 1,2007 2,80092,8009 3,60013 $5,200 (22, 8,400) (23, 9,200) (24, 8,800) (26, 10,400) (27, 10,600)

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Solution 1

To answer this question, we need to understand the rate at which Steven's savings account balance is increasing each month.

From the given table, we can see that the balance increases by 800everytwomonths.Thisiscalculatedbysubtractingthebalanceofthefirstmonthfromthebalanceofthethirdmonth(800 every two months. This is calculated by subtracting the balance of the first month from the balance of the third month (1200 - 400=400 = 800) and dividing by the difference in months (3 - 1 = 2). So, the rate of increase is $400 per month.

Now, we can use this rate to check which of the given points will lie on the line.

  1. (22, 8,400): By the 22nd month, the balance should be 22 * 400=400 = 8,800. So, this point will not lie on the line.
  2. (23, 9,200): By the 23rd month, the balance should be 23 * 400=400 = 9,200. So, this point will lie on the line.
  3. (24, 8,800): By the 24th month, the balance should be 24 * 400=400 = 9,600. So, this point will not lie on the line.
  4. (26, 10,400): By the 26th month, the balance should be 26 * 400=400 = 10,400. So, this point will lie on the line.
  5. (27, 10,600): By the 27th month, the balance should be 27 * 400=400 = 10,800. So, this point will not lie on the line.

So, the correct answers are (23, 9,200) and (26, 10,400).

This problem has been solved

Solution 2

To answer this question, we need to determine the rate at which Steven's savings account balance is increasing each month.

From the given table, we can see that the balance increases by 800everytwomonths,or800 every two months, or 400 per month.

Now, we can use this rate to check which of the given points will lie on the line.

  1. (22, 8,400): By the 22nd month, Steven's balance should be 22 * 400=400 = 8,800. So, this point will not lie on the line.

  2. (23, 9,200): By the 23rd month, Steven's balance should be 23 * 400=400 = 9,200. So, this point will lie on the line.

  3. (24, 8,800): By the 24th month, Steven's balance should be 24 * 400=400 = 9,600. So, this point will not lie on the line.

  4. (26, 10,400): By the 26th month, Steven's balance should be 26 * 400=400 = 10,400. So, this point will lie on the line.

  5. (27, 10,600): By the 27th month, Steven's balance should be 27 * 400=400 = 10,800. So, this point will not lie on the line.

So, the correct answers are (23, 9,200) and (26, 10,400).

This problem has been solved

Solution 3

To answer this question, we need to determine the rate at which Steven's savings account balance is increasing each month.

From the given table, we can see that the balance increases by 800every2months,whichmeansthebalanceincreasesby800 every 2 months, which means the balance increases by 400 each month.

Now, let's check the given points:

  1. (22, 8,400): If Steven's balance increases by 400eachmonth,thenhisbalanceafter22monthsshouldbe22∗400 each month, then his balance after 22 months should be 22 * 400 = $8,800. So, this point will not lie on the line.

  2. (23, 9,200): After 23 months, the balance should be 23 * 400=400 = 9,200. So, this point will lie on the line.

  3. (24, 8,800): After 24 months, the balance should be 24 * 400=400 = 9,600. So, this point will not lie on the line.

  4. (26, 10,400): After 26 months, the balance should be 26 * 400=400 = 10,400. So, this point will lie on the line.

  5. (27, 10,600): After 27 months, the balance should be 27 * 400=400 = 10,800. So, this point will not lie on the line.

So, the correct answers are (23, 9,200) and (26, 10,400).

This problem has been solved

Solution 4

To answer this question, we first need to understand the rate at which Steven's savings account balance is increasing each month.

From the table, we can see that the balance increases by 800everytwomonths.Thismeansthebalanceincreasesby800 every two months. This means the balance increases by 400 each month.

Now, let's check each of the given points:

  1. (22, 8,400): By the 22nd month, the balance should be 22 * 400=400 = 8,800. So, this point is not on the line.
  2. (23, 9,200): By the 23rd month, the balance should be 23 * 400=400 = 9,200. So, this point is on the line.
  3. (24, 8,800): By the 24th month, the balance should be 24 * 400=400 = 9,600. So, this point is not on the line.
  4. (26, 10,400): By the 26th month, the balance should be 26 * 400=400 = 10,400. So, this point is on the line.
  5. (27, 10,600): By the 27th month, the balance should be 27 * 400=400 = 10,800. So, this point is not on the line.

So, the correct answers are (23, 9,200) and (26, 10,400).

This problem has been solved

Solution 5

To answer this question, we need to determine the rate at which Steven's savings account balance is increasing each month.

From the given table, we can see that the balance increases by 800everytwomonths,or800 every two months, or 400 per month.

Now, we can use this rate to check which of the given points will lie on the line.

  1. (22, 8,400): After 22 months, the balance should be 22 * 400=400 = 8,800. So, this point will not lie on the line.
  2. (23, 9,200): After 23 months, the balance should be 23 * 400=400 = 9,200. So, this point will lie on the line.
  3. (24, 8,800): After 24 months, the balance should be 24 * 400=400 = 9,600. So, this point will not lie on the line.
  4. (26, 10,400): After 26 months, the balance should be 26 * 400=400 = 10,400. So, this point will lie on the line.
  5. (27, 10,600): After 27 months, the balance should be 27 * 400=400 = 10,800. So, this point will not lie on the line.

So, the correct answers are (23, 9,200) and (26, 10,400).

This problem has been solved

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