A função é definida por F(x)=ax+b sabe-se que F(-2)=6 e F(-4)=-8. Qual o valor de F(6)?
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Solução!
![f(x)=y\\\\\
y=ax+b](https://tex.z-dn.net/?f=f%28x%29%3Dy%5C%5C%5C%5C%5C%0Ay%3Dax%2Bb "f(x)=y\\\\\
y=ax+b")
Fazendo um sistema linear para determinarmos uma reta.
![\begin{cases}
-2a+b=6\\
-4a+b=-8
\end{cases}\\\\\\\
\begin{cases}
-2a+b=6.(-1)\\
-4a+b=-8
\end{cases}\\\\\\\
\begin{cases}
2a-b=-6\\
-4a+b=-8
\end{cases}\\\\\\\
2a-4a=-6-8\\\\\
-2a=-14\\\\\
a= \dfrac{-14}{-2}\\\\\\
\boxed{a=7}](https://tex.z-dn.net/?f=%5Cbegin%7Bcases%7D%0A-2a%2Bb%3D6%5C%5C%0A-4a%2Bb%3D-8%0A%5Cend%7Bcases%7D%5C%5C%5C%5C%5C%5C%5C%0A%0A%5Cbegin%7Bcases%7D%0A-2a%2Bb%3D6.%28-1%29%5C%5C%0A-4a%2Bb%3D-8%0A%5Cend%7Bcases%7D%5C%5C%5C%5C%5C%5C%5C%0A%5Cbegin%7Bcases%7D%0A2a-b%3D-6%5C%5C%0A-4a%2Bb%3D-8%0A%5Cend%7Bcases%7D%5C%5C%5C%5C%5C%5C%5C%0A2a-4a%3D-6-8%5C%5C%5C%5C%5C%0A-2a%3D-14%5C%5C%5C%5C%5C%0Aa%3D+%5Cdfrac%7B-14%7D%7B-2%7D%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7Ba%3D7%7D+ "\begin{cases}
-2a+b=6\\
-4a+b=-8
\end{cases}\\\\\\\
\begin{cases}
-2a+b=6.(-1)\\
-4a+b=-8
\end{cases}\\\\\\\
\begin{cases}
2a-b=-6\\
-4a+b=-8
\end{cases}\\\\\\\
2a-4a=-6-8\\\\\
-2a=-14\\\\\
a= \dfrac{-14}{-2}\\\\\\
\boxed{a=7}")
![-2a+b=6\\\\\
-2(7)+b=6\\\\\
-14+b=6\\\\\\
b=6+14\\\\\\
\boxed{b=20}](https://tex.z-dn.net/?f=-2a%2Bb%3D6%5C%5C%5C%5C%5C%0A-2%287%29%2Bb%3D6%5C%5C%5C%5C%5C%0A-14%2Bb%3D6%5C%5C%5C%5C%5C%5C%0Ab%3D6%2B14%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7Bb%3D20%7D "-2a+b=6\\\\\
-2(7)+b=6\\\\\
-14+b=6\\\\\\
b=6+14\\\\\\
\boxed{b=20}")
Montemos a equação da reta para determinar f(6)!
![f(x)=ax+b\\\\\
f(x)=7x+20\\\\\\
f(6)=7.(6)+20\\\\\\
f(6)=42+20\\\\\
\boxed{f(6)=62}](https://tex.z-dn.net/?f=f%28x%29%3Dax%2Bb%5C%5C%5C%5C%5C%0Af%28x%29%3D7x%2B20%5C%5C%5C%5C%5C%5C%0Af%286%29%3D7.%286%29%2B20%5C%5C%5C%5C%5C%5C%0Af%286%29%3D42%2B20%5C%5C%5C%5C%5C%0A%5Cboxed%7Bf%286%29%3D62%7D "f(x)=ax+b\\\\\
f(x)=7x+20\\\\\\
f(6)=7.(6)+20\\\\\\
f(6)=42+20\\\\\
\boxed{f(6)=62}")
Bom dia!
Bons estudos!
Solução!
Fazendo um sistema linear para determinarmos uma reta.
Montemos a equação da reta para determinar f(6)!
Bom dia!
Bons estudos!
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