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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?

Down 15
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1 answer

To compare the two pricing models, let's analyze them:

  1. The first business charges $22 per t-shirt, which gives us 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, leading to the equation: \[ y = 16x + 15 \]

The first graph (from the first business) is a linear equation that passes through the origin (0,0) because there is no fixed fee. The second graph has a y-intercept of \(15\) because of the setup fee.

To transform the first graph into a non-proportional graph that has the same y-intercept as the second graph, we need to shift the first graph down by the setup fee of $15. This means you should subtract 15 from the total cost of the first business's graph.

So, the transformation needed is:

  • Down 15

This will change the first equation to: \[ y = 22x - 15 \] This new equation is non-proportional (due to the -15) and has the same y-intercept as \(y = 16x + 15\) at \(x = 0\) (both will be at (0,15)).

Answer:

Down 15