The relationship described, where cost \( y \) is directly proportional to the number of items purchased \( x \) with each item costing $1, can be expressed as the equation \( y = kx \), where \( k \) is the constant of proportionality (in this case, \( k = 1 \)).
This means that when you buy 1 item, the cost is $1 (1 unit), when you buy 2 items, the cost is $2 (2 units), and so on, leading to a linear relationship that passes through the origin \( (0,0) \).
Looking at the options provided:
- Option 1 does not pass through the origin; it starts at \( (1, 0) \).
- Option 2 passes through the origin \( (0, 0) \) and the points \( (1, 1) \), \( (3, 3) \), and \( (5, 5) \), which fits the direct proportionality of \( y = x \).
- Option 3 starts at \( (0, 1) \), which is not correct for this type of relationship.
- Option 4 does not pass through the origin and has negative values for \( x \), which is also incorrect.
Therefore, the correct graph that shows the direct proportional relationship is the second option:
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 \( (5, 5) \).
3 answers