Question

Find an expression for the function f(x) whose graph is a line passing through the points (6,-1) and (-3,-2). F(x) =

Answer 1

Explanation:

f(x) = ax+b

passing through the point (6,-1) : when x = 6 f(x) = -1

means : -1 = a (6)+b

passing through the point (-3,-2) : when x = -3 f(x) = -2

means : --2 = a (-3)+b

you have the system :: 6a +b = - 1......(1)

-3a +b = -2........(2)

by (1) : b = -1 - 6a

by (2) : b = -2+3a

so : -2+3a = -1 - 6a

3a+6a =2 -1

9a =1 a =1/9 put the value of a in (1) or (2) : -3(1/9)+b = - 2

-1/3 +b = - 2

b = -2+1/3

b = -5/3

f(x) = 1/9 x - 5/3