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??
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.
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.
To transform the first graph into a non-proportional graph with the same y-intercept as the second graph, you would need to introduce a fixed additional cost per t-shirt on top of the proportional charge.
In the first scenario, the equation for the cost of t-shirts (y) can be represented as y = 12x, where x represents the number of t-shirts ordered. This equation is proportional because the cost of t-shirts increases directly in proportion to the number of t-shirts ordered.
In the second scenario, the equation for the cost of t-shirts (y) can be represented as y = 11x + 20, where x again represents the number of t-shirts ordered. This equation is non-proportional because there is an additional fixed setup fee of $20 regardless of the number of t-shirts ordered.
To transform the first graph to match the y-intercept of the second graph, you need to add a fixed cost of $20 to the proportional equation. This can be done by modifying the equation to y = 12x + 20.
By introducing the fixed cost of $20, the first graph becomes non-proportional, with the same y-intercept as the second graph.
To transform the first graph to make it become non-proportional with the same y-intercept as the second graph, we can introduce a fixed cost or a one-time set-up fee in addition to the per-unit cost of $12.
Let's denote the number of t-shirts as x and the total cost as y.
In the first scenario, where there is only a per-unit cost of $12, the equation representing the cost is:
y = 12x
If we want to introduce a fixed cost or a set-up fee equivalent to $20, we can add this fixed cost to the equation which will make it non-proportional. So the new equation will be:
y = 12x + 20
Now, on a graph, you would plot the points for different values of x and y using the new equation, y = 12x + 20. By doing so, you will see that the resulting graph will have the same y-intercept as the second graph. However, the graph will not be a proportional relationship as it includes a fixed cost in addition to the per-unit cost.
By introducing the fixed cost or set-up fee, the graph changes from being a straight line (proportional) to a line with a positive slope (non-proportional).