Question

A medical clinic is reducing the number of incoming patients by giving vaccines before flu season. During week 5 of flu season, the clinic saw 85 patients. In week 10 of flu season, the clinic saw 65 patients. Assume the reduction in the number of patients each week is linear. Write an equation in function form to show the number of patients seen each week at the clinic.

A.f(x) = 20x + 85
B.f(x) = −20x + 85
C.f(x) = 4x + 105
D.f(x) = −4x + 105

Answer 1

Answer: D or f(x) = -4x + 105

Answer 2

D.f(x) = −4x + 105

Explanation:

Since the function in linear, we know it has a slope.

We know 2 points

(5,85) and (10,65) are 2 points on the line

m = (y2-y1)/(x2-x1)

= (65-85)/(10-5)

=-20/5

=-4

We know a point and the slope, we can use point slope form to write the equation

y-y1 =m(x-x1)

y-85 = -4(x-5)

Distribute

y-85 = -4x+20

Add 85 to each side

y-85+85 = -4x+20+85

y = -4x+105

Changing this to function form

f(x) =-4x+105