6. One business charges $12 per t-shirt custom made.
Another business charges $11 per t-shirt plus a $20 set up fee for custom made.
If you were to graph both of these scenarios on the coordinate plane, the first graph would be proportional and the second non proportional.
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
Left 1
Left 1
Right 1
Right 1
Left 20
Left 20
Right 20
Right 20
Up 1
Up 1
Up 20
Up 20
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The correct answer is: Up 20
To transform the first graph to make it become a non-proportional graph with the same y-intercept as the second graph, you would need to increase the slope of the first graph.
Since the second graph has a $20 set up fee added to the cost of each t-shirt, you would need to increase the cost of each t-shirt in the first graph by $20 as well. This means that you need to add $20 to the cost per t-shirt in the first graph.
To do this, you would need to move the points on the first graph upwards by $20. This can be achieved by going "Up 20" for each point on the first graph.
To transform the first graph from being proportional to non-proportional while maintaining the same y-intercept as the second graph, you would need to increase the slope (or steepness) of the line in the first graph. This can be achieved by increasing the rate of change in the relationship between the x and y variables.
In this case, the y-intercept remains the same, meaning that the initial cost for custom-made t-shirts is $20. To increase the slope, we can consider the pricing difference between the two businesses. The first business charges a flat rate of $12 per t-shirt, while the second business charges $11 per t-shirt plus a $20 set up fee.
We can express this difference as the additional cost of the second business compared to the first business, which is $11 (per t-shirt). So, for every additional $11 spent on t-shirts, the second business adds a flat $20 set up fee. To convert this into a slope, we can calculate the ratio of the set up fee to the additional cost per t-shirt.
The ratio is given by:
Set up fee ($20) / Additional cost ($11) = 20/11 ≈ 1.818
The ratio represents the increase in cost (y-value) for every unit increase in the number of t-shirts (x-value). Thus, to transform the first graph into a non-proportional graph with the same y-intercept, you would need to adjust the slope by multiplying the slope of the original graph by the ratio.
For example, if the original slope was 2 (meaning for every 1 t-shirt, the cost increases by $2), you would multiply this slope by the ratio:
Adjusted slope = Original slope (2) * Ratio (1.818) ≈ 3.636
Now, the transformed graph will have a steeper slope and will no longer be proportional while maintaining the same y-intercept as the second graph.