F(x) = (a-2)x+b+3
f(-1) =2 f(3) = -4
a.b=? i need it with the explanation : )

a = 1/2 and   b = - 5/2

Step-by-step explanation:

F(x) = (a-2)x+b+3

f(-1) =2  means  :  (a-2)(-1)+b+3  = 2

-a+2 +b+3 =2

-a+b = -3 (1)

f(3) = -4  means  :  (a-2)(3)+b+3  = -4

3a-6+b+3 =-4

3a+b =-1 (2)

the system is : -a+b = -3 (1)

                        3a+b =-1 (2)

by(1) : b = a - 3

by (2) : b = -3a -1

so : -3a-1 = a -3

-4a = -2

a = 1/2

b = 1/2 -3

b = - 5/2

anathor solution let : a-2 =m    m the slope of this line

m = (-4-2)/(3-(-1))  = -6/4 = -3/2

a-2 = -3/2

so : a = 2-3/2     a = 1/2

f(x) =-3/2 x +b+3

f(-1) =2

(-3/2)(-1)+b+3 = 2

b = -3-3/2+2

b = -5/2

your mode is the one that occurs the most which is -7