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Difficulty: MediumLinear Functions and Graphs

An online retailer uses a linear relationship to determine the shipping cost of an order based on the total weight of the items in the order. The table below shows the shipping cost, yy, in dollars, for an order with a total weight of xx pounds.

Weight (xx pounds)Shipping Cost (yy dollars)
229.509.50
6617.5017.50

What is the shipping cost, in dollars, for an order with a total weight of 1111 pounds?

Answer: 27.5

Answer

The correct shipping cost for an order weighing 11 pounds is 27.5 dollars.
The linear relationship has a constant rate of change (slope). Using the coordinates from the table, (2,9.50)(2, 9.50) and (6,17.50)(6, 17.50), the slope mm is calculated as 17.50−9.506−2=84=2\frac{17.50 - 9.50}{6 - 2} = \frac{8}{4} = 2. Using the point-slope form, the equation of the line is y−9.50=2(x−2)y - 9.50 = 2(x - 2), which simplifies to y=2x+5.50y = 2x + 5.50. Substituting x=11x = 11 gives y=2(11)+5.50=27.5y = 2(11) + 5.50 = 27.5.

Step-by-Step Solution

1
Calculate the slope (rate of change) of the linear relationship.
m=2m = 2
Determines the rate at which the shipping cost increases per additional pound of weight.
2
Formulate the linear equation representing the relationship.
y=2x+5.50y = 2x + 5.50
Establishes a functional relationship to calculate costs for any given weight.
3
Evaluate the function at the target weight of 11 pounds.
y=27.5y = 27.5
Determines the final cost of shipping for the specified weight of 11 pounds.

Key Concept

Determining and evaluating linear functions represented in tabular form
Estimated Time:1m 30s
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Topics

Linear Functions and Graphs

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