Question

Emma hired a contractor to install a new brick patio in her backyard. The original quote was $832, but as the contractor was installing the patio, Emma realized she wanted it to be wider. The cost of expanding the patio is $13 per square foot. You can use a function to describe the total cost of the patio if she decides to expand it by x square feet. Write an equation for the function. If it is linear, write it in the form f(x)=mx+b. If it is exponential, write it in the form f(x)=a(b)x.

Answer 1

Answer: The linear function representing the total cost of the patio is:

f(x) = 13x + 832

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