Question

dada a funçao f(x)=ax +b .calcule os valores de a e b de forma que f(2) = 4 e f(-3) = -6 .Desta forma podemos afirmar que :
a) f(x) = -2x+3
b) f(x) = -3x+2
c) f(x) = 2x
d) f(x) = -2x

Answer 1

f(2) = 4 e f(-3) = -6 

2a + b = 4
-3a +b = - 6(-1)

2a + b = 4
3a -b =  6
     5a = 10
a = 2

a=2
P(2,4)

2.2 + b = 4
     b = 4 - 4
   b = 0

Y = 2x + 0   ==> Y = 2x

Answer 2

$\begin{vmatrix}x&y&1\\2&4&1\\-3&-6&1\end{vmatrix}=0\\\\\\\begin{bmatrix}x&y&1&|&x&y\\2&4&1&|&2&4\\-3&-6&1&|&-3&-6\end{bmatrix}=0\\\\4x-3y-12+12+6x-2y=0\\\\10x-5y=0\\\\5y=10x\\\\\boxed{y=2x}$