In this scenario, the cost \( y \) is directly proportional to the number of items purchased \( x \) at a cost of $1 per item. This means that the relationship can be expressed as:
\[ y = kx \]
where \( k \) is the constant of proportionality. In this case, since each item costs $1, \( k = 1 \). Therefore, the equation simplifies to:
\[ y = x \]
This implies that when you purchase 0 items, the cost \( y \) is $0; when you purchase 1 item, the cost is $1; when you purchase 2 items, the cost is $2; and so forth.
Looking at the provided graph options, the correct graph will be the one that shows a line passing through the origin (0,0) with a slope of 1, which means it increases equally in both x and y directions.
The correct response is:
A graph with the x-axis and y-axis ranging from 0 to 5 in increments of 1 shows a line ending with an arrow. The line passes through the points (0, 0), (1, 1), (3, 3), and (5, 5).
This graph illustrates the direct proportionality between \( x \) and \( y \) correctly.