Question

Leah receives a piggy bank containing 20 dollars for her birthday. Every week, Leah adds 10 dollars to the piggy bank. Represent this situation with a table, a graph, and an equation.
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 20
1 30
2 40
3 50
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
5
10
15
20
25
30
35
40
45
50
Time in weeks
Dollars in the piggy bank
Rate of change:

Answer 1

To determine the rate of change, we need to find out how much the amount of money in the piggy bank increases each week.

From the problem, we know:
- Initially, Leah starts with $20 in her piggy bank.
- Each week, she adds $10.

The rate of change is the amount added to the piggy bank per week, which is $10.

### Rate of Change:
**Rate of change = $10 per week**

### Now let's summarize the information:

#### Table
| Time in weeks | Dollars in the piggy bank |
|---------------|---------------------------|
| 0 | 20 |
| 1 | 30 |
| 2 | 40 |
| 3 | 50 |

#### Equation
The equation that represents this situation can be modeled using a linear equation in the form:
\[
y = mx + b
\]
where:
- \(y\) is the amount of money in the piggy bank,
- \(m\) is the rate of change (the amount added per week),
- \(x\) is the number of weeks, and
- \(b\) is the initial amount in the piggy bank.

Given:
- \(m = 10\) (the amount added each week)
- \(b = 20\) (the initial amount)

The equation would be:
\[
y = 10x + 20
\]

### Summary
- The rate of change is $10 per week.
- The equation that represents the amount in the piggy bank over time is \( y = 10x + 20 \).