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Answer :
Answer: The linear function representing the total cost of the patio is:
f(x) = 13x + 832
Step-by-step explanation:
The total cost of the patio consists of the original quote and the additional cost for expanding it by x square feet. Since the cost of expanding the patio is given in dollars per square foot, this relationship is linear. We can write a linear function in the form f(x) = mx + b, where:
- f(x) represents the total cost of the patio.
- m is the slope (rate of change) of the function, which corresponds to the cost per square foot of expanding the patio.
- x is the number of additional square feet Emma decides to expand the patio.
- b is the y-intercept, representing the original quote.
In this case, the slope m is $13 per square foot, and the y-intercept b is the original quote of $832. So the linear function representing the total cost of the patio is:
f(x) = 13x + 832
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