We are given two data points: (20, 132) and (30, 221). We can use these points to find the equation of the line that represents the linear function of the cost y in terms of the number of people x.
First, we need to find the slope of the line. We can use the formula:
slope = (change in y) / (change in x)
Using the two data points, we get:
slope = (221 - 132) / (30 - 20) = 89 / 10
Next, we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
where m is the slope, and (x1, y1) is a point on the line. We can use either of the two data points as (x1, y1). Let's use (20, 132):
y - 132 = (89/10)(x - 20)
Simplifying this equation, we get:
y = (89/10)x - 220/5
or
y = (89/10)x - 44
This equation gives us the cost y in terms of the number of people x.
To find the cost for 79 people, we can substitute x = 79 into the equation:
y = (89/10)(79) - 44 = 708.1
So the cost for a birthday party for 79 people would be approximately $708.10.