A prepaid cell phone charges a preset number of minutes to use text messaging. The graph represents y, the number of minutes used for x, the number of text messages sent and received. Is there a direct variation? Which equation represents the relationship?

Question

Yes, y = 2x.
Yes, y = 20x.
No, y = x + 10.
No, y = x + 20.

Answer 1

To determine if there is direct variation between the number of minutes used (y) and the number of text messages sent and received (x), we need to see if the relationship can be expressed in the form \( y = kx \), where \( k \) is a constant.

Let's analyze the provided options:

1. Yes, y = 2x.
   This equation represents a direct variation with a constant \( k = 2 \).

2. Yes, y = 20x.
   This equation also represents a direct variation with a constant \( k = 20 \).

3. No, y = x + 10.
   This equation does not represent direct variation, as it includes a constant term (10) which indicates a non-zero y-intercept.

4. No, y = x + 20.
   This equation also does not represent direct variation for the same reason as the previous one (a non-zero y-intercept).

So, the correct answers regarding direct variation are the equations \( y = 2x \) and \( y = 20x \).

To answer your query: Yes, there is a direct variation. The options that represent the relationship are \( y = 2x \) and \( y = 20x \).