Question

Represente graficamente a função cujo gráfico é a reta que passa pelos pontos A(4,2) e B(2,8) e determine a taxa de variação da função.

Answer 1

$\Large\boxed{\begin{array}{l}\underline{\rm Coeficiente~angular~da~reta}\\\underline{\rm que~passa~por~A(x_A,y_A)~e~B(x_B,y_B)}\\\sf m=\dfrac{y_B-y_A}{x_B-x_A}\\\\\underline{\rm Equac_{\!\!,}\tilde ao~da~reta~que~passa}\\\underline{\rm pelo~ponto~P(x_0,y_0)~e~tem}\\\underline{\rm coeficiente~angular~m}\\\sf y=y_0+m\cdot(x- x_0)\end{array}}$

$\Large\boxed{\begin{array}{l}\underline{\rm C\acute alculo~do~coeficiente~angular~m\!:}\\\sf m=\dfrac{8-2}{2-4}\\\\\sf m=\dfrac{6}{-2}=-3\\\sf Vamos~adotar~o~ponto~A(4,2).\\\sf y=2+(-3)\cdot(x-4)\\\sf y=2-3x+12\\\sf y=-3x+14\end{array}}$