If f(x) is a linear function and given f(2) =−4 and f(11)=1, determine the linear function.

Question

If f(x) is a linear function and given f(2) =−4 and f(11)=1, determine the linear function.

c.) What is f(x)? 

Answer 1

f(2) =-4 is the point (2,-4)

f(11) = 1 is the point (11,1)

a line through those two points has slope = m = (1- -4)/(11-2) = 5/9

use a point slope formula, using either point

(y-1)/(x-11) = 5/9

y-1 = (5/9)(x-11) = 5x/9 - 55/9

y = 5x/9 - 46/9

f(x) = 5x/9 -46/9 is the linear function where f(2) =-4 and f(11) = 1

9y- 9 = 5x -55

9y -5x = -46 is the equation of the line that satisfies f(2)=-4 and f(11)=1