Ask a New Question
Menu

Kelly opens a savings account with 30 dollars she got for her graduation. Every month, Kelly adds 15 dollars to the account. 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 savings account after 0, 1, 2, and 3 months.
Time in months Dollars in the savings account
0
1
2
3
You got it!
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 Dollars in the savings account
0 30
1 45
2 60
3 75
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 account. Start by finding the rate of change. In other words, by how much does the number of dollars in the savings account change for every month?
t
y
0
1
2
3
4
5
6
7
8
9
10
0
7.5
15
22.5
30
37.5
45
52.5
60
67.5
75
Time in months
Dollars in the savings account
Rate of change:

1 answer

To represent Kelly's savings account situation:

Table Representation

We will calculate the amount in the savings account after each specified month:

  • Initial Amount: $30
  • Monthly Addition: $15

| Time in Months | Dollars in the Savings Account | |----------------|-------------------------------| | 0 | 30 | | 1 | 30 + 15 × 1 = 45 | | 2 | 30 + 15 × 2 = 60 | | 3 | 30 + 15 × 3 = 75 |

Completed Table

| Time in Months | Dollars in the Savings Account | |----------------|-------------------------------| | 0 | 30 | | 1 | 45 | | 2 | 60 | | 3 | 75 |

Points to Plot

The points to plot on the coordinate plane are:

  • (0, 30)
  • (1, 45)
  • (2, 60)
  • (3, 75)

Equation Representation

To formulate the equation of the linear function, we will use the slope-intercept form of a linear equation:

\[ y = mx + b \]

Where:

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

Finding the Rate of Change (m):

  • The monthly increase is $15. Therefore,

\[ m = 15 \]

Finding the Initial Amount (b):

  • The amount when \( t = 0 \) is $30.

Thus, the equation becomes:

\[ y = 15t + 30 \]

Summary

  • Rate of Change: $15 per month
  • Initial Amount: $30
  • Equation: \( y = 15t + 30 \)

Kelly's savings can be represented as a table, plotted as points on a graph, and expressed with this linear equation.