Neil started with 250 dollars in his savings account. Every month, Neil spends 25 dollars from his savings account at the grocery store. Represent this situation with a table, a graph, and an equation.

Question

Let’s start by representing this situation with a table. Start by finding the amount in the account after 0, 1, 2 and 3 months.
Time in months Number of dollars in the account
0
1
2
3
Great job!
Plot the points below on the coordinate plane to represent the amount in the account after 0, 1, 2, and 3 months.
Time in months Number of dollars in the account
0 250
1 225
2 200
3 175
Good work!
We can connect the points you just graphed with a line. To find the equation that represents this linear function, you’ll need the rate of change and the initial amount in the account. Start by finding the rate of change. In other words, by how much does the amount in the savings account change each month?
t
y
0
1
2
3
4
5
0
25
50
75
100
125
150
175
200
225
250
Time in months
Number of dollars in the account
Rate of change:

Answer 1

To analyze Neil's savings account situation, let’s summarize the information we have and calculate the necessary elements step-by-step.

Step 1: Create the table

| Time in months (t) | Number of dollars in the account (y) | |---------------------|---------------------------------------| | 0 | 250 | | 1 | 225 | | 2 | 200 | | 3 | 175 |

1. At 0 months, he has $250.
2. At 1 month, after spending $25, he has $250 - $25 = $225.
3. At 2 months, he has $225 - $25 = $200.
4. At 3 months, he has $200 - $25 = $175.

Step 2: Plotting the points

The points that represent his savings account balance over time are:

• (0, 250)
• (1, 225)
• (2, 200)
• (3, 175)

Step 3: Rate of Change

The rate of change is the amount Neil spends from his savings account each month.

• He spends $25 each month, so the rate of change is -25 (negative because his savings decrease).

Step 4: Linear Function Equation

The general equation for a linear function can be represented as: \[ y = mx + b \] where:

• \( m \) is the slope (rate of change),
• \( b \) is the y-intercept (initial amount).

Given:

• The initial amount \( b = 250 \) (when \( t = 0 \)),
• The rate of change \( m = -25 \) (since he spends $25 each month).

Putting it all together, the equation representing Neil's savings account balance over time is: \[ y = -25t + 250 \]

Summary

• Table shows the balance after 0, 1, 2, and 3 months.
• Graph plots the points (0, 250), (1, 225), (2, 200), (3, 175).
• Equation representing the situation is \( y = -25t + 250 \).

If you have any more questions or need further assistance, feel free to ask!