Answer:
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
