Tyler receives a piggy bank containing 3 dollars for his birthday. Every week, Tyler adds 6 dollars to the piggy bank. 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 piggy bank after 0, 1, 2, and 3 weeks.
Time in weeks Dollars in the piggy bank
0
1
2
3
Excellent!
Plot the points below on the coordinate plane to represent the amount in the piggy bank after 0, 1, 2, and 3 weeks.
Time in weeks Dollars in the piggy bank
0 3
1 9
2 15
3 21
You got it!
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 piggy bank. Start by finding the rate of change. In other words, by how much does the number of dollars in the piggy bank change for every week?
t
y
0
1
2
3
4
5
6
7
8
9
10
0
3
6
9
12
15
18
21
24
27
30
Time in weeks
Dollars in the piggy bank
Rate of change:

Answer 1

To represent Tyler's savings situation, we can analyze it step by step.

Step 1: Create a table

We will calculate the amount of money in the piggy bank after 0, 1, 2, and 3 weeks.

| Time in weeks | Dollars in the piggy bank | |---------------|---------------------------| | 0 | 3 | | 1 | 3 + 6 = 9 | | 2 | 9 + 6 = 15 | | 3 | 15 + 6 = 21 |

Thus, the completed table looks like this:

| Time in weeks | Dollars in the piggy bank | |---------------|---------------------------| | 0 | 3 | | 1 | 9 | | 2 | 15 | | 3 | 21 |

Step 2: Graph the points

Now we will plot the following points based on the data we've gathered:

• (0, 3)
• (1, 9)
• (2, 15)
• (3, 21)

Step 3: Determine the equation

To find the equation that represents this linear function, we need the rate of change and the initial amount.

• Initial amount (y-intercept) when \( t = 0 \): 3 dollars.
• Rate of change: This is the amount added to the piggy bank each week, which is 6 dollars per week.

The general form of a linear equation is \( y = mx + b \), where:

• \( m \) is the rate of change (slope)
• \( b \) is the y-intercept

For this situation:

• \( m = 6 \)
• \( b = 3 \)

Final Equation:

So the equation that models this situation is: \[ y = 6t + 3 \]

Where:

• \( y \) = total dollars in the piggy bank
• \( t \) = time in weeks

Summary:

• Rate of change: 6 dollars per week
• Equation: \( y = 6t + 3 \)