To determine which graph best represents the relationship between the number of weeks (x) and the total number of new words learned (y), we can establish the equation based on the information given.
The student learns 15 new words each week, so the relationship can be expressed as:
\[ y = 15x \]
Where:
- \( y \) is the total number of new words learned,
- \( x \) is the number of weeks in the program.
This equation describes a linear relationship with a slope of 15 and a y-intercept of 0. This means that the graph will be a straight line that starts at the origin (0,0) and rises steadily, increasing by 15 for each additional week.
When selecting the correct graph:
- Look for a straight line that starts at the origin.
- The line should have a positive slope, indicating that the number of words learned increases as weeks increase.
- The slope should be relatively steep (15 words per week), showing significant growth.
If you have options for graphs labeled a, b, c, and d, select the one that meets these criteria. If you provide details or descriptions of those graphs, I can help you analyze them further!