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Question about Graphs of Proportional Relationships

Math

Originais Teachy

Graphs of Proportional Relationships

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(Originais Teachy 2023) - Question Medium of Math

A company produces T-shirts and the cost of production is directly proportional to the number of T-shirts produced. Suppose the company represented this proportional relationship on a graph with cost on the y-axis and the number of T-shirts on the x-axis. If the graph passes through points (0,0) and (100, 500), explain how you would determine the unit rate of the cost per T-shirt and what the graph would look like. Furthermore, discuss how you would use the graph to predict the cost of producing different quantities of T-shirts.
a.
The unit rate of the cost per T-shirt is $5. The graph is a straight line that passes through the points (0,0) and (100, 500), with a slope of 5. To predict the cost of producing different quantities of T-shirts, find the y-value on the y-axis, go straight across to the line, and then go vertically to the x-axis to find the corresponding x-value (number of T-shirts).
b.
The unit rate of the cost per T-shirt is $5. The graph is a straight line that passes through the points (0,0) and (100, 500), with a slope of 5. To predict the cost of producing different quantities of T-shirts, find the x-value on the x-axis, go straight up to the line, and then go horizontally to the y-axis to find the corresponding y-value (cost).
c.
The unit rate of the cost per T-shirt is $10. The graph is a straight line that passes through the points (0,0) and (100, 500), with a slope of 10. To predict the cost of producing different quantities of T-shirts, find the x-value on the x-axis, go straight up to the line, and then go horizontally to the y-axis to find the corresponding y-value (cost).
d.
The unit rate of the cost per T-shirt is $5. The graph is a curve that passes through the points (0,0) and (100, 500). To predict the cost of producing different quantities of T-shirts, find the x-value on the x-axis, go straight up to the curve, and then go horizontally to the y-axis to find the corresponding y-value (cost).
e.
The unit rate of the cost per T-shirt is $3. The graph is a straight line that passes through the points (0,0) and (100, 500), with a slope of 3. To predict the cost of producing different quantities of T-shirts, find the x-value on the x-axis, go straight up to the line, and then go horizontally to the y-axis to find the corresponding y-value (cost).

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