Based on the scenario you've provided, it looks like you're trying to fill in a table where 'x' represents the number of days and 'y' represents the number of texts sent during that period. Let's deduce the values step by step.
You mentioned that you send 50 texts every 2 days. Therefore, the rate of text sending can be calculated as follows:
-
Determine Rate of Texts per Day:
- 50 texts every 2 days means: \[ \text{Rate} = \frac{50 \text{ texts}}{2 \text{ days}} = 25 \text{ texts per day} \]
-
Fill in the Table Entries:
- For \( x = 0 \) days: \( y = 25 \times 0 = 0 \)
- For \( x = 2 \) days (2 days): \( y = 25 \times 2 = 50 \)
- For \( x = 4 \) days (4 days): \( y = 25 \times 4 = 100 \)
- For \( x = 6 \) days (6 days): \( y = 25 \times 6 = 150 \)
- For \( x = 8 \) days (8 days): \( y = 25 \times 8 = 200 \)
- For \( x = 10 \) days (10 days): \( y = 25 \times 10 = 250 \)
- Continuing this for \( x=12 \), \( x=14 \), \( x=16 \), \( x=18 \), \( x=20 \) days:
- \( x = 12 \): \( y = 300 \)
- \( x = 14 \): \( y = 350 \)
- \( x = 16 \): \( y = 400 \)
- \( x = 18 \): \( y = 450 \)
- \( x = 20 \): \( y = 500 \)
-
Identifying Missing Values in the table (since provided values need to fill in):
- a: In the entries, you have
a
as the value of days, which based on the above findings can be filled:- For x = 4, it corresponds to y = 100
- b: Given the context, let's say the missing value for
b
is referring tox = 8
days, which corresponds toy = 200
. - c: The missing value for
c
is thus0
forx=0
. - d: The value for
d
would be the value at60
days as per the relation we've built, thusy = 25 * 12 = 300
.
- a: In the entries, you have
Thus the filled table should look as:
| x - # of days | y - # of texts | |---------------|-----------------| | 0 | 0 | | 2 | 50 | | 4 | 100 | | 6 | 150 | | 8 | 200 | | 10 | 250 | | 12 | 300 |
With the responses:
- a = 4,
- b = 8,
- c = 0,
- d = 300.
For the response selection related options such as "linear relationship," the equation of the line reflecting the rate would be \( y = 25x \), which is indeed a linear relationship with a slope of 25, iterating through the correct values should maintain this structure.