Camille receives a piggy bank containing 4 dollars for her birthday. Every week, Camille adds 8 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
You got it!
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 4
1 12
2 20
3 28
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 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
4
8
12
16
20
24
28
32
36
40
Time in weeks
Dollars in the piggy bank
Rate of change:
You got it!
Now, find the initial amount. What is the initial number of dollars in the piggy bank?
t
y
0
1
2
3
4
5
6
7
8
9
10
0
4
8
12
16
20
24
28
32
36
40
Time in weeks
Dollars in the piggy bank
Rate of change: 8
Initial amount:
You got it!
Now that you have the rate of change and the initial number of dollars in the piggy bank, you can write an equation to represent this linear function. Start by writing an equation in words.
t
y
0
1
2
3
4
5
6
7
8
9
10
0
4
8
12
16
20
24
28
32
36
40
Time in weeks
Dollars in the piggy bank
Rate of change: 8
Initial amount: 4

Dollars in
the piggy bank
=
Initial number
of dollars
+
Change in
dollars
Nice!
Now that you wrote this equation in words, represent this equation mathematically. The amount in the piggy bank is what we’re trying to find, so we can represent that with the variable y.
t
y
0
1
2
3
4
5
6
7
8
9
10
0
4
8
12
16
20
24
28
32
36
40
Time in weeks
Dollars in the piggy bank
Rate of change: 8
Initial amount: 4

Dollars in
the
piggy bank = Initial
number
of dollars + Change in
dollars

y
=
+
Nice!
Next, record the initial number of dollars in the piggy bank.
t
y
0
1
2
3
4
5
6
7
8
9
10
0
4
8
12
16
20
24
28
32
36
40
Time in weeks
Dollars in the piggy bank
Rate of change: 8
Initial amount: 4

Dollars in
the
piggy bank = Initial
number
of dollars + Change in
dollars
y =
+
Great job!
Now, record the change in the number of dollars in the piggy bank by multiplying the change in dollars per week by the number of weeks. You can represent the number of weeks with the variable t.
t
y
0
1
2
3
4
5
6
7
8
9
10
0
4
8
12
16
20
24
28
32
36
40
Time in weeks
Dollars in the piggy bank
Rate of change: 8
Initial amount: 4

Dollars in the
piggy bank = Initial
number
of dollars + Change in dollars
y = 4 +
·
Change in dollars per week Number of weeks

Answer 1

Let's summarize the situation you've described about Camille's piggy bank with a table, a graph, and an equation.

Table

We can represent the amount of money Camille has after 0, 1, 2, and 3 weeks:

| Time in Weeks (t) | Dollars in the Piggy Bank (y) | |--------------------|-------------------------------| | 0 | 4 | | 1 | 12 | | 2 | 20 | | 3 | 28 |

Graph

You can plot the points from the table on a coordinate plane:

• (0, 4)
• (1, 12)
• (2, 20)
• (3, 28)

Graph Description

The x-axis represents time in weeks, and the y-axis represents the dollars in the piggy bank. When you connect these points with a line, it shows a linear relationship.

Rate of Change and Initial Amount

• Rate of change: 8 (This represents the amount of money added each week)
• Initial amount: 4 (This is how much Camille initially has in the piggy bank)

Equation in Words

Dollars in the piggy bank = Initial number of dollars + Change in dollars

Equation Mathematically

To represent this as an equation mathematically:

1. The initial amount is 4 dollars.
2. The change in dollars per week is given by multiplying the rate of change (8 dollars) by the number of weeks (t).

So the equation becomes: \[ y = 4 + 8t \]

where:

• \( y \) = Dollars in the piggy bank
• \( t \) = Time in weeks

In summary:

• The amount in Camille's piggy bank after t weeks can be calculated using the equation \( y = 4 + 8t \).