To transform the first graph (proportional) into a non-proportional graph with the same y-intercept as the second graph, we need to introduce additional fixed costs that are not dependent on the number of t-shirts.
In the first scenario, the cost per t-shirt is $12, so the equation for this graph would be y = 12x, where y represents the total cost and x represents the number of t-shirts.
In the second scenario, the cost per t-shirt is $11 plus a $20 set up fee. The equation for this graph would be y = 11x + 20.
To make the first graph non-proportional while keeping the same y-intercept as the second graph, we can introduce a fixed cost of $20 in the proportional scenario. This fixed cost will remain the same regardless of the number of t-shirts.
So, the equation for the transformed graph would be y = 12x + 20.
By adding the fixed cost of $20, the transformed graph becomes non-proportional as it now includes a fixed component in addition to the variable cost per t-shirt.
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??
3 answers
would I move the 20 left, right, or up?
Apologies for the confusion in my previous response. To transform the first graph into a non-proportional graph with the same y-intercept as the second graph, you would move the graph up by adding a fixed cost.
In the second scenario, the equation for the graph is y = 11x + 20, where 20 represents the fixed setup fee.
To make the first graph non-proportional and have the same y-intercept, you would add the same fixed cost to the equation for the first graph. The equation would then be y = 12x + 20, where 20 represents the fixed cost that is added to each t-shirt.
By adding the fixed cost of 20, the graph is shifted upward, providing a non-proportional relationship between the total cost and the number of t-shirts while maintaining the same y-intercept as the second graph.
In the second scenario, the equation for the graph is y = 11x + 20, where 20 represents the fixed setup fee.
To make the first graph non-proportional and have the same y-intercept, you would add the same fixed cost to the equation for the first graph. The equation would then be y = 12x + 20, where 20 represents the fixed cost that is added to each t-shirt.
By adding the fixed cost of 20, the graph is shifted upward, providing a non-proportional relationship between the total cost and the number of t-shirts while maintaining the same y-intercept as the second graph.