Question

determine a funçao afim f(x)=ax+b, sabendo que f(1) = 5 e f(-3)=-7

Answer 1

f(1)= a.1+b
a.1+b = 5

f(-3)= a.(-3)+b
a.(-3)+b = -7

a+b = 5
b= 5-a

-3a+b = -7
-3a+5-a = -7
-3a-a+ -7-5
-4a = -12
4a = 12
a= 12/4
a= 3

a+b= 5
3+b = 5
b=2

Answer 2

f(x) = ax + b

f(1) = 5

f(-3) = - 7

f(1) = a.1 + b
5 = a + b
a + b = 5

¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
f(-3) = - 7

f(x) = ax + b
f(-3) = a.(-3) + b
- 7 = - 3a + b
- 3a + b = - 7

   a + b = 5      
- 3a + b = - 7  (- 1)

   a + b = 5
 3a - b = 7  (+)
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4a = 12
a = 12/4
a = 3

a + b = 5
3 + b = 5
b = 5 - 3
b = 2

a = 3 e b = 2

f(x) = ax + b

R.:
f(x) = 3x + 2