Question

Determine a equação da reta na forma reduzida que contém os pontos (2,1) e (4,7)

Answer 1

$\large\boxed{\begin{array}{l}\underline{\rm Coeficiente\,angular}\\\sf Dados\,os\,pontos\,A(x_A,y_A)\,e\,B(x_B,y_C)\\\sf de~\!\!finimos\,coeficiente\,angular\,como\,sendo\\\sf m=\dfrac{y_B-y_A}{x_B-x_A}\\\underline{\sf equac_{\!\!,}\tilde ao\,da\,reta\,que\,tem\,coeficiente\,angular\,m}\\\underline{\sf e\,passa\,pelo\,ponto~P(x_0,y_0)}\\\sf y=y_0+m\cdot(x-x_0)\end{array}}$

$\Large\boxed{\begin{array}{l}\sf A(2,1)~B(4,7)\\\sf m=\dfrac{y_B-y_A}{x_B-x_A}\\\\\sf m=\dfrac{7-1}{4-2}\\\\\sf m=\dfrac{6}{2}\\\\\sf m=3\\\sf adotando\,o\,ponto~A(2,1)~temos:\\\sf y=1+3\cdot(x-2)\\\sf y=1+3x-6\\\huge\boxed{\boxed{\boxed{\boxed{\boxed{\sf y=3x-5}}}}}\end{array}}$