Months:1,2,4,7
Total Cost ($):57,74,108,159
b) What is the equation for
Power Fitness? [2pts]
(Provide the equation in y = mx + b form)
Type equation here
To find the equation for Power Fitness, we can use the given data points (months, total cost). Let's assign the months as the x-values and the total cost as the y-values.
Using the slope-intercept form equation, y = mx + b, where m is the slope and b is the y-intercept, we need to determine the values of m and b.
First, let's calculate the slope:
m = (change in y) / (change in x)
Between months 1 and 2:
m1 = (74 - 57) / (2 - 1) = 17
Between months 2 and 4:
m2 = (108 - 74) / (4 - 2) = 34
Between months 4 and 7:
m3 = (159 - 108) / (7 - 4) = 17
The average slope is (17 + 34 + 17) / 3 = 22.67
Next, let's determine the y-intercept. We can choose any data point to solve for b, but let's use the data point (1, 57).
Using the point-slope form equation, y - y1 = m(x - x1):
y - 57 = 22.67(x - 1)
Expanding the bracket:
y - 57 = 22.67x - 22.67
Simplifying:
y = 22.67x + 34.67
Therefore, the equation for Power Fitness in y = mx + b form is:
y = 22.67x + 34.67