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?

option:

A). Up 4

B). Right 4

C). Left 15

D). Down 15

E). Up 15

F). Down 4

Answer 1

To compare the two businesses, we can analyze their pricing structures:

1. The first business charges $22 per t-shirt. This can be represented by the equation:
\[
y = 22x
\]
where \(y\) is the total cost and \(x\) is the number of t-shirts.

2. The second business charges $16 per t-shirt plus a $15 setup fee. This can be represented by the equation:
\[
y = 16x + 15
\]

In this comparison, the first business's cost per t-shirt is constant and does not have a fixed fee, making it a proportional relationship. In contrast, the second business's cost includes a fixed fee ($15) along with a variable cost, making it a non-proportional relationship due to the y-intercept being $15.

To transform the first business's graph (which is proportional) into a non-proportional graph with the same y-intercept as the second business (which is 15), we need to adjust the entire graph of the first business downwards to have the same starting point.

Since the original proportional graph starts at 0 (y-intercept), we need to move it down:

\[
y = 22x \text{ becomes } y = 22x - 15.
\]

This means we should shift the graph down by $15 to match the y-intercept of the second graph.

Thus, the correct option is:

**D). Down 15**.