To determine the correct graph representing the relationship where the cost for using the internet is proportional to the time used at a rate of $2 per hour, we need to identify a graph that depicts a linear relationship where:
- The cost \( y \) is equal to \( 2 \times x \), where \( x \) is the number of hours.
- The relationship implies that when \( x = 0 \), \( y = 0 \) (no cost for 0 hours).
- As \( x \) increases, \( y \) increases proportionally.
Evaluating the options provided:
-
First graph: Passes through the points \( (0, 0) \), \( (1, 2) \), and \( (2, 4) \). This graph correctly represents the relationship, as \( (1, 2) \) corresponds to 1 hour costing $2 and \( (2, 4) \) corresponds to 2 hours costing $4.
-
Second graph: Passes through the points \( (0, 0) \), \( (2, 1) \), \( (4, 2) \), and \( (6, 3) \). This graph does not represent the correct relationship since these points do not reflect the cost structure of $2 per hour.
-
Third graph: Passes through points \( (0, 0) \), \( (2, -1) \), and \( (4, -2) \). This graph does not represent a valid cost relationship, as costs cannot be negative.
-
Fourth graph: Passes through points \( (0, 0) \), \( (1, -2) \), and \( (2, -4) \). Similar to the third graph, this does not represent a valid cost relationship.
The correct answer is the first graph, as it correctly represents that the cost is $2 per hour with points showing a linear increase consistent with that rate.
11 answers