Question

Write a linear function f with the values f (6) = 8 and f (9) = 3.

Answer 1

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

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

So, the equation of linear function is

$y-8=\dfrac{3-8}{9-6}(x-6)$

$y-8=\dfrac{-5}{3}(x-6)$

$y-8=-\dfrac{5}{3}(x)-\dfrac{5}{3}(-6)$

$y-8=-\dfrac{5}{3}(x)+10$

Add 8 on both sides.

$y=-\dfrac{5}{3}(x)+10+8$

$y=-\dfrac{5}{3}(x)+18$

Function form is,

$f(x)=-\dfrac{5}{3}(x)+18$

Therefore, the required linear function is $f(x)=-\dfrac{5}{3}(x)+18$.