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The table shows the cost, c, of making different numbers of shirts, t. Create an equation to model the cost.

Number of Shirts, t 100 250 500
Cost to Company, c $600.00 $1,387.50 $2,700.00

User Ben Golden
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1 Answer

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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!

User TJR
by
8.2k points

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