To determine the correct graph representing the relationship where cost (y) is proportional to time (x) at a rate of $2 per hour, we can analyze how the cost changes with time.
The relationship can be expressed as: \[ y = 2x \] Where:
- \( y \) is the cost in dollars
- \( x \) is the time in hours
Thus, the points on the graph for 0 to 6 hours would be:
- At \( x = 0 \): \( y = 2(0) = 0 \)
- At \( x = 1 \): \( y = 2(1) = 2 \)
- At \( x = 2 \): \( y = 2(2) = 4 \)
- At \( x = 3 \): \( y = 2(3) = 6 \)
- At \( x = 4 \): \( y = 2(4) = 8 \)
- At \( x = 5 \): \( y = 2(5) = 10 \)
- At \( x = 6 \): \( y = 2(6) = 12 \)
We are specifically looking for a graph that represents these points and shows a linear relationship starting from (0, 0) and going up to at least (6, 12) or higher at appropriate increments.
In reviewing the choices:
- The first graph seems to have increments that correspond to lower values (not aligning with $2 per hour).
- The second graph shows points that are incorrect for our linear equation.
- The third and fourth graphs show negative values, which do not match our requirement of costs being positive.
Based on this analysis, none of the graphs listed perfectly fit the criteria set out by the relationship \( y = 2x \). However, if the first graph's cost axis were extended to represent the true values correctly (up to \( y = 12 \)), it would be suitable.
If the first graph has the misrepresentation of values, let the cost axis be indicative of y-values representing doubling hour values correctly, in a correct scaling, that would make it the most fitting option if only looking for a valid starting point through \( (0,0) \).
So, if selecting based on the best fit for the proportionality:
- Select the first graph; it seems to imply a relationship, even though it does not go high enough for A valid y-value for every hour compared to what we expect with a proper scaling.