Respuesta :
Given two points [tex] (x_1,y_1) [/tex] and [tex] (x_2,y_2) [/tex], the line passing through them is given by
[tex] \dfrac{x-x_2}{x_1-x_2} = \dfrac{y-y_2}{y_1-y_2} [/tex]
In your case, [tex] (x_1,y_1)=(2,1) [/tex] and [tex] (x_2,y_2) = (5,-8)[/tex]
So, the equation of the line becomes
[tex] \dfrac{x-5}{2-5} = \dfrac{y+8}{1+8} \iff \dfrac{x-5}{-3} = \dfrac{y+8}{9} \iff 9(x-5) = -3(y+8) [/tex]
If we expand both sides, we have
[tex] 9x-45 = -3y -24 [/tex]
Add 24 to both sides:
[tex] 9x-21 = -3y [/tex]
Divide both sides by -3:
[tex] y=-3x+7 [/tex]
