To transform the first graph (which represents the business charging $12 per t-shirt) into a non-proportional graph with the same y-intercept as the second graph (which has a $20 setup fee), you need to introduce a fixed cost.
The equation for the first business can be expressed as:
\[ y = 12x \]
where \( y \) is the total cost and \( x \) is the number of t-shirts.
The equation for the second business can be expressed as:
\[ y = 11x + 20 \]
To make the first graph non-proportional while maintaining the same y-intercept of $20, you can add a fixed cost (setup fee) to the first equation. The result will be:
\[ y = 12x + 20 - 12(0) \] or simply, \[ y = 12x + 20 - 12x_0 \]
However, to clarify the transformation with a clear understanding of the y-intercept, you can modify it directly:
- Start with the original equation \( y = 12x \).
- Shift it vertically by adding a constant amount, in this case, \( 20 \).
So the transformed equation becomes:
\[ y = 12x + 20 \]
This new equation is non-proportional (due to the presence of the fixed cost) and has the same y-intercept (which is \( 20 \), the point where the graph intersects the y-axis).
In summary, by adding a fixed setup fee of $20 to the cost of custom t-shirts, you've successfully transformed the initial proportional graph into a non-proportional one, maintaining the same y-intercept.
3 answers