At the store, the cost of every item is $1

Question

. Cost, y, is directly proportional to the number of items purchased, x. Identify the graph that shows this proportional relationship.(1 point)
Responses

A graph with the x-axis and y-axis ranging from 0 to 3 in unit increments shows a line ending with an arrow. The line begins at the plotted point left parenthesis 0 comma 1 right parenthesis; then passes through left parenthesis 1 comma 2 right parenthesis; and left parenthesis 2 comma 3 right parenthesis.
Image with alt text: A graph with the x-axis and y-axis ranging from 0 to 3 in unit increments shows a line ending with an arrow. The line begins at the plotted point left parenthesis 0 comma 1 right parenthesis; then passes through left parenthesis 1 comma 2 right parenthesis; and left parenthesis 2 comma 3 right parenthesis.

A graph with the x-axis and y-axis ranging from 0 to 3 in unit increments shows a line ending with an arrow. The line passes through the points left parenthesis 1 comma 0 right parenthesis; left parenthesis 2 comma 1 right parenthesis; and left parenthesis 3 comma 2 right parenthesis.
Image with alt text: A graph with the x-axis and y-axis ranging from 0 to 3 in unit increments shows a line ending with an arrow. The line passes through the points left parenthesis 1 comma 0 right parenthesis; left parenthesis 2 comma 1 right parenthesis; and left parenthesis 3 comma 2 right parenthesis.

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 left parenthesis 0 comma 0 right parenthesis; left parenthesis 1 comma 1 right parenthesis; left parenthesis 3 comma 3 right parenthesis; and left parenthesis 5 comma 5 right parenthesis.
Image with alt text: 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 left parenthesis 0 comma 0 right parenthesis; left parenthesis 1 comma 1 right parenthesis; left parenthesis 3 comma 3 right parenthesis; and left parenthesis 5 comma 5 right parenthesis.

A graph with the x-axis ranging from 0 to negative 3 in unit decrements and the y-axis ranging from 0 to 3 in unit increments shows a line ending with an arrow. The line passes through the points left parenthesis negative 1 comma 1 right parenthesis; left parenthesis negative 2 comma 2 right parenthesis; and left parenthesis negative 3 comma 3 right parenthesis.
Image with alt text: A graph with the x-axis ranging from 0 to negative 3 in unit decrements and the y-axis ranging from 0 to 3 in unit increments shows a line ending with an arrow. The line passes through the points left parenthesis negative 1 comma 1 right parenthesis; left parenthesis negative 2 comma 2 right parenthesis; and left parenthesis negative 3 comma 3 right parenthesis.
Remaining Attempts : 3
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Answer 1

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.