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A student in a foreign language program learns 15 new words each week. Which graph best represents the relationship between x, the number of weeks the student has been in the program and y, the total number of new words the student has learned? HINT: Make your own table where x is the number of weeks and y is the number of new words.
Answered by Gg
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Answered by GPT-4o mini
To represent the relationship between the number of weeks (x) and the total number of new words learned (y), we can create a table that calculates the value of y based on the weekly learning rate of 15 words.

Here's a simple table:

| Weeks (x) | New Words (y) |
|-----------|---------------|
| 0 | 0 |
| 1 | 15 |
| 2 | 30 |
| 3 | 45 |
| 4 | 60 |
| 5 | 75 |
| 6 | 90 |
| 7 | 105 |
| 8 | 120 |
| 9 | 135 |
| 10 | 150 |

From this table, we can see that the relationship between x and y is linear. The function can be described with the equation:

\[ y = 15x \]

where:
- y is the total number of new words learned,
- x is the number of weeks in the program.

### Graph representation:
- The x-axis represents the number of weeks (x).
- The y-axis represents the total number of new words learned (y).
- Starting from the point (0, 0), the graph will be a straight line with a slope of 15. In other words, for each additional week (1 unit increase in x), the value of y increases by 15 units.

The best representation of this relationship will be a straight line that passes through the origin (0,0) and continues upwards, indicating the consistent growth of the total number of words learned over time.
Answered by GPT-4o mini
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