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Ava started with 90 dollars in her savings jar. Every week, Ava spends 9 dollars from her savings jar at the grocery store. 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 jar after 0, 1, 2 and 3 weeks.
Time in weeks Number of dollars in the savings jar
0
1
2
3
Good work!
Plot the points below on the coordinate plane to represent the amount in the savings jar after 0, 1, 2, and 3 weeks.
Time in weeks Number of dollars in the savings jar
0 90
1 81
2 72
3 63
Nice!
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 amount in the savings jar change each week?
t
y
0
1
2
3
4
5
0
9
18
27
36
45
54
63
72
81
90
Time in weeks
Number of dollars in the savings jar
Rate of change:

1 answer

To find the rate of change in Ava's savings jar, we can determine how much the total amount decreases each week, which is given as 9 dollars.

Rate of Change:

  • The amount in the savings jar decreases by 9 dollars per week, so the rate of change is -9 dollars per week.

Now, let's summarize everything:

Table:

| Time in weeks | Number of dollars in the savings jar | |---------------|---------------------------------------| | 0 | 90 | | 1 | 81 | | 2 | 72 | | 3 | 63 |

Graph Points:

The points to plot on the coordinate plane based on the table above would be:

  • (0, 90)
  • (1, 81)
  • (2, 72)
  • (3, 63)

Equation:

To write an equation that represents the amount of money \(y\) in the savings jar after \(t\) weeks, we can use the equation of a line:

\[ y = mx + b \]

Where:

  • \(m\) is the slope (or rate of change), which we found to be -9.
  • \(b\) is the initial amount in the savings jar, which is 90.

Thus, the equation becomes:

\[ y = -9t + 90 \]

Summary:

  • Rate of change: -9 dollars per week
  • Table of values (shown above)
  • Points to plot based on the table
  • Equation: \(y = -9t + 90\)