Question

escreva a equaçao reduzida da reta que passa pelos pontos A(5,2) e B(-1,3)?

Answer 1

y=ax+b

 

2=5a+b

3=-a+b subtraindo

 

-1=6a

a=-1/6

 

b=3+a

b=3-1/6

b=17/6

 

y=-1/6x+17/6

Answer 2

$\begin{vmatrix} x & y & 1 \\ 5 & 2 & 1 \\ - 1 & 3 & 1 \end{vmatrix} = 0 \\\\ \begin{vmatrix} x & y & 1 & | & x & y \\ 5 & 2 & 1 & | & 5 & 2 \\ - 1 & 3 & 1 & | & - 1 & 3 \end{vmatrix} = 0 \\\\ 2x - y + 15 + 2 - 3x - 5y = 0 \\ - 6y - x + 17 = 0 \\ 6y = - x + 17 \\ \boxed{y = - \frac{x}{6} + \frac{17}{6}}$