One business charges $22 per T-shirt that is custom made. Another business charge is $16 per day surplus a $15 said if a forecast of my T-shirts how would you transform the first graph to make it become a non-proportional graph with the same y-intercept as a second graph.
To transform the first graph into a non-proportional graph with the same y-intercept as the second graph, we need to introduce a fixed cost to the first business' pricing model. This fixed cost will ensure that the graph does not remain directly proportional.
Let's assume that the second business charges a fixed cost of $x per purchase in addition to the daily surplus charge of $16. In this case, the equation for the second business' pricing model can be written as:
Cost = $16/day + $15 + $x
Now, to make the first graph non-proportional but with the same y-intercept as the second graph, we need to determine the fixed cost to add to the first business' pricing model.
Since the y-intercept represents the cost when no T-shirts are purchased, we can equate the y-intercepts of both the first and second graphs.
For the first business, the y-intercept is at $0, as there is no fixed cost mentioned. Therefore, the equation for the first business' pricing model is simply:
Cost = $22/T-shirt
Setting this equation equal to the y-intercept of the second graph, which is $15, we have:
$22/T-shirt = $15
Solving for T-shirt, we find:
T-shirt = $15 * (1/$22) ≈ 0.682
Rounding to the nearest whole number, we get T-shirt = 1.
This indicates that the first business charges $22 per T-shirt and has a y-intercept of $0 (no fixed cost).
Now, to have the same y-intercept as the second graph, which is $15, we need to add a fixed cost of $15 to the first business' pricing model. Thus, the transformed equation for the first business' pricing model becomes:
Cost = $22/T-shirt + $15
With this modification, the first graph becomes non-proportional with 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 add a constant fee to the $22 per T-shirt charge.
Let's assume the second business charges a constant fee of $x per forecast of T-shirts. To make the y-intercept the same as the second graph (which has a $15 fee), we can set x = 15.
Therefore, to transform the first graph into a non-proportional graph with the same y-intercept as the second graph, the new equation would be:
Cost = $22 per T-shirt + $15 per forecast
or
Cost = $22T + $15
This new equation still starts at the same point as the second graph (y-intercept) but has a different rate of increase as the number of T-shirts increases.
To transform the first graph into a non-proportional graph with the same y-intercept as the second graph, you need to adjust the equation of the first graph.
Let's start by defining the equation for the first graph, where the cost (C) is a function of the number of T-shirts (x):
C = 22x
To make this equation non-proportional, we can introduce a constant term (b) in addition to the variable term (mx), where m represents the slope of the line. In this case, we want the y-intercept (where x is zero) to be the same as the second graph, which is $15.
So, the adjusted equation for the first graph would be:
C = mx + b
Since the y-intercept is $15, we set b = 15. Now we need to determine the value of m (slope) to fit the data.
To find the slope, we need two points from the second graph. Let's assume the second graph represents the number of days (d) given the number of T-shirts (x). We have the points (0, 15) and (1, 31).
The slope (m) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
m = (31 - 15) / (1 - 0)
m = 16 / 1
m = 16
Now, we can substitute the values of m and b into the adjusted equation:
C = 16x + 15
This equation represents a non-proportional graph with the same y-intercept as the second graph.