Answer:
f(x) = -6x + 120
Explanation:
Step-by-step explanation: To write an equation in function form that represents the number of patients seen each week at the clinic, we need to consider the given information. We are told that the reduction in the number of patients each week is linear. Let's use the given information to find the slope (rate of change) and the y-intercept of the linear equation. The clinic saw 90 patients in week 5 and 60 patients in week 10. To find the slope, we can use the formula: slope = (y2 - y1) / (x2 - x1) Using the points (5, 90) and (10, 60), we can calculate the slope: slope = (60 - 90) / (10 - 5) = -30 / 5 = -6 Now that we have the slope, we need to find the y-intercept. We can choose any point on the line to do this. Let's use the point (5, 90). The equation of a line in slope-intercept form is given by: y = mx + b Where m is the slope and b is the y-intercept. Substituting the values we have: 90 = -6(5) + b Simplifying: 90 = -30 + b Adding 30 to both sides: 90 + 30 = b b = 120 Now we have the slope (-6) and the y-intercept (120). Substituting these values into the equation of a line, we get: f(x) = -6x + 120 So, the correct equation in function form to show the number of patients seen each week at the clinic is: f(x) = -6x + 120