Answer: c=(5.25)t+75
Explanation:
To solve this problem, we need to think of this as a graph. First, we find the slope of our two coordinate points. There are three given: (100,600) (250,1387.5) and (500,2700)
We know that the number of shirts will be x in this equation because it is the independent variable. The cost to the company depends on the number of shirts made.
I like to choose whole numbers because they are the easiest to work with. Therefore, I will choose the coordinates (100,600) and (500,2700)
Now we use the slope formula:
2700-600/500-100
=2100/400
=5.25
To check to make sure that the slope is consistent throughout, we can look at our other coordinate: (250,1387.5)
Use the slope formula to check:
1387.5-600/250-100
=787.5/150
=5.25
Now we know that we have a consistent slope, the next step is to find the y-intercept.
(You could also use the point-slope formula, which would give you the entire equation outright. Although it is faster, there is more potential for an accidental mistake, so I like to use this method, although this method will be a bit slower.)
To find the y-intercept with a slope and point, use the equation y=mx+b.
y=(5.25)x+b
Now we can take a point and substitute it in. I'm going to use the point (100,600) as it is the easiest one.
600=5.25(100)+b
600=525+b
b=600-525
=75
Therefore, the equation is c=(5.25)t+75.
Good luck on your homework!