To determine how to transform the graph of the first business to match the characteristics of the second business, we start with the cost equations for both businesses:
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Business A (charges $22 per t-shirt): \[ C = 22x \] Here, \( C \) is the total cost and \( x \) is the number of t-shirts.
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Business B (charges $16 per t-shirt plus $15 setup fee): \[ C = 16x + 15 \]
The main feature of interest is that Business A's graph is proportional, while Business B's graph is not due to the $15 setup fee.
To create a non-proportional graph with the same y-intercept as Business B’s graph, we need to adjust Business A's equation, specifically by introducing a fixed cost. The y-intercept of Business B is $15 (when \( x = 0 \)), which means we want to adjust Business A's graph so that it also has this y-intercept.
Business A currently has a y-intercept of \( 0 \) (when \( x = 0 \), \( C = 0 \)). To change this to have a y-intercept of $15, we need to shift the graph of Business A up by $15. Thus, we can adjust the cost equation for Business A to be:
\[ C = 22x + 15 \]
By doing this transformation, we have made it a non-proportional graph (due to the additional fixed cost of $15) with the desired y-intercept.
So, the correct transformation is to move the graph up 15.
Answer: Up 15
3 answers