Question

One business charges $22 per t-shirt that is custom made.

Another business charges $16 per t-shirt plus a $15 set up fee for custom made t-shirts.

How would you transform the first graph to make it become a non proportional graph with the same y-intercept as the second graph?

(1 point)
Responses

Up 4
Up 4

Left 15
Left 15

Right 4
Right 4

Down 4
Down 4

Down 15
Down 15

Up 15

Answer 1

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:

1. Business A (charges $22 per t-shirt):
\[ C = 22x \]
Here, \( C \) is the total cost and \( x \) is the number of t-shirts.

2. 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**