The relationship given states that the cost \( y \) is directly proportional to the number of items purchased \( x \), where the cost of each item is $1. This means that:
\[ y = kx \]
Where \( k \) is the constant of proportionality. In this case, since each item costs $1, \( k = 1 \). Therefore, the equation simplifies to:
\[ y = x \]
The graph of this equation is a straight line that passes through the origin (0, 0) and has a slope of 1. It will also pass through points like (1, 1), (2, 2), (3, 3), etc.
From the options provided, the option that matches this description 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 correctly represents the direct proportionality of cost to the number of items purchased.
1 answer