Question

Over the summer, you text a bunch. Let’s say you make 50 texts every 2 days.

Drag and drop

Fill in the missing parts of the table:




x - # of days 0 3 7 12
y - # of texts Response area 75 175 Response area
This is a Response area relationship because it is Linear with the y-intercept at Response area

Answer 1

To fill in the missing parts of the table and describe the relationship, let’s analyze the information provided:

Given that you send 50 texts every 2 days, we can determine the rate of texts sent per day:

- **Rate of texts per day**:
\( \frac{50 \text{ texts}}{2 \text{ days}} = 25 \text{ texts per day} \)

We can now use this rate to compute the values of \( y \) (the number of texts) for each \( x \) (the number of days):

1. For \( x = 0 \):
\[
y = 25 \cdot 0 = 0
\]

2. For \( x = 3 \):
\[
y = 25 \cdot 3 = 75
\]

3. For \( x = 7 \):
\[
y = 25 \cdot 7 = 175
\]

4. For \( x = 12 \):
\[
y = 25 \cdot 12 = 300
\]

Now the table filled out will look like:

| x - # of days | 0 | 3 | 7 | 12 |
|---------------|----|----|-----|-----|
| y - # of texts | 0 | 75 | 175 | 300 |

Finally, to describe the relationship:

This is a **linear** relationship because it follows the form \( y = mx + b \), where \( m \) (the slope, which is 25 texts per day) is constant, and \( b \) (the y-intercept) is 0 (when \( x = 0 \), \( y = 0 \)).

So, the complete statement would be:

This is a **linear** relationship because it is linear with the **y-intercept at 0**.