Jenna receives a piggy bank containing 8 dollars for her birthday. Every week, Jenna adds 4 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
Good work!
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 8
1 12
2 16
3 20
Excellent!
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
2
4
6
8
10
12
14
16
18
20
Time in weeks
Dollars in the piggy bank
Rate of change:

Answer 1

To represent the situation, let's start by completing the table for the amount in Jenna's piggy bank after 0, 1, 2, and 3 weeks.

Table

| Time in weeks | Dollars in the piggy bank | |---------------|---------------------------| | 0 | 8 | | 1 | 12 | | 2 | 16 | | 3 | 20 |

Explanation of the values:

• At week 0, Jenna has the initial 8 dollars.
• She adds 4 dollars each week:
  • After 1 week: \( 8 + 4 = 12 \)
  • After 2 weeks: \( 8 + 4 \times 2 = 16 \)
  • After 3 weeks: \( 8 + 4 \times 3 = 20 \)

Now that we've established the amounts for the table, we can plot the points on a coordinate plane with time in weeks on the x-axis and dollars in the piggy bank on the y-axis.

Coordinates for the Graph

| Time in weeks | Dollars in the piggy bank | |---------------|---------------------------| | 0 | 8 | | 1 | 12 | | 2 | 16 | | 3 | 20 |

The points to plot are:

• (0, 8)
• (1, 12)
• (2, 16)
• (3, 20)

Rate of Change

Next, we need to calculate the rate of change. The rate of change represents how much the dollars in the piggy bank increase each week.

Jenna adds 4 dollars every week, so the rate of change is 4 dollars per week.

Equation

Now we can write the equation that represents this linear function. The general formula for a linear equation is:

\[ y = mx + b \]

Where:

• \( y \) is the total amount in the piggy bank,
• \( m \) is the rate of change,
• \( x \) is the time in weeks,
• \( b \) is the initial amount (the y-intercept).

Given the rate of change (m) is 4 dollars per week and the initial amount (b) is 8 dollars, the equation becomes:

\[ y = 4x + 8 \]

Thus, we now have a complete representation of the situation in a table, as graph points, and in equation form.