Given:
Two values of a linear function are f (6) = 8 and f (9) = 3.
To find:
The linear function.
Solution:
According to the question f (6) = 8 and f (9) = 3, it means the function passes through (6,8) and (9,3).
If a linear function passes through two points then the equation is
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
So, the equation of linear function is
[tex]y-8=\dfrac{3-8}{9-6}(x-6)[/tex]
[tex]y-8=\dfrac{-5}{3}(x-6)[/tex]
[tex]y-8=-\dfrac{5}{3}(x)-\dfrac{5}{3}(-6)[/tex]
[tex]y-8=-\dfrac{5}{3}(x)+10[/tex]
Add 8 on both sides.
[tex]y=-\dfrac{5}{3}(x)+10+8[/tex]
[tex]y=-\dfrac{5}{3}(x)+18[/tex]
Function form is,
[tex]f(x)=-\dfrac{5}{3}(x)+18[/tex]
Therefore, the required linear function is [tex]f(x)=-\dfrac{5}{3}(x)+18[/tex].
