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

Step-by-step 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