Use the image to answer the question.
A line graph shows number of items on the x-axis and cost in dollars on the y-axis. The graph shows the trends for A, B, C, and D. The x-axis ranges from 0 to 7 in increments of 1. The y-axis ranges from 0 to 35 in increments of 5. A line starts at the origin and passes through the plotted point A at left parenthesis 1 comma 25 right parenthesis. A line starts at the origin and passes through plotted point B at left parenthesis 2 comma 30 right parenthesis. A line starts at the origin and passes through plotted point C at left parenthesis 2 comma 20 right parenthesis. A line starts at the origin and passes through plotted point D at left parenthesis 4 comma 20 right parenthesis.
Talia noticed a sale at her favorite store. The points on the graph show how many items she bought of each. T-shirts were selling for $5 each, long sleeve shirts were $10 each, jeans were discounted to $15 each, and sweaters were on sale for $25 each. Name the point corresponding to the number of pairs of jeans Talia purchased.
(1 point)
Responses
B
B
C
C
A
A
D
D
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The point corresponding to the number of pairs of jeans Talia purchased can be determined by matching the cost of the jeans to the correct line on the graph.
The graph shows cost on the y-axis, so we are looking for the cost at which each point is plotted. Jeans were discounted to $15 each, so we can look for a line that has a slope reflecting the price of $15 per item.
Point D is plotted at (4, 20). Given that each pair of jeans costs $15, we can calculate the number of jeans Talia could have bought for $20:
Number of jeans = Total cost / Cost per jeans = $20 / $15 per jean
Since the total cost ($20) isn't a multiple of the cost per jean ($15), this tells us that point D cannot correspond to jeans, as you cannot buy a fraction of a jeans pair.
Point C is plotted at (2, 20). This would suggest that for $20, Talia could buy:
Number of jeans = $20 / $15 per jean = 1.33 (approximately)
Again, as you cannot buy a fraction of a pair of jeans, this indicates that point C also does not correspond to the jeans.
Point B is plotted at (2, 30). This point suggests that for $30, Talia could buy:
Number of jeans = $30 / $15 per jean = 2
This result is a whole number, which makes sense since you can buy two pairs of jeans for $30 at a price of $15 each. Hence, point B corresponds to the purchase of jeans.
Therefore, the correct response is B.