Emma hired a contractor to install a new brick patio in her backyard. The original quote was $832. However, Emma decided to make the patio wider. The cost of expanding the patio is $13 per square foot.

Write an equation for the function that describes the total cost of the patio if she decides to expand it by $x$ square feet. If the function is linear, write it in the form [tex]f(x) = mx + b[/tex]. If it is exponential, write it in the form [tex]f(x) = a(b)^x[/tex].

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