Answer:
[tex]f(x) = -6x +120[/tex]
Step-by-step explanation:
Let's call y the number of patients treated each week
Let's call x the week number.
If the reduction in the number of patients each week is linear then the equation that models this situation will have the following form:
[tex]y = mx + b[/tex]
Where m is the slope of the equation and b is the intercept with the x-axis.
If we know two points on the line then we can find the values of m and b.
We know that During week 5 of flu season, the clinic saw 90 patients, then we have the point:
(5, 90)
We know that In week 10 of flu season, the clinic saw 60 patients, then we have the point:
(10, 60).
Then we can find m and b using the followings formulas:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] and [tex]b=y_1-mx_1[/tex]
In this case: [tex](x_1, y_1) = (5, 90)[/tex] and [tex](x_2, y_2) = (10, 60)[/tex]
Then:
[tex]m=\frac{60-90}{10-5}[/tex]
[tex]m=-6[/tex]
And
[tex]b=90-(-6)(5)[/tex]
[tex]b=120[/tex]
Finally the function that shows the number of patients seen each week at the clinic is:
[tex]f(x) = -6x +120[/tex]
