Question

1.Escreva a equação da reta determinada por: a)A(2,3) e B(0,1),     b)M(-3,1) e N(2,-5),                  c) P(-1,-2) e Q(5,2) d), d) R(3,4) e T(-6,8), e(S(5,-2) e Z(-6,-2)

Answer 1

a)A(2,3) e B(0,1),         y = 1.x + 1    crescente
a= 1-3 = - 2 ==> a= 1
     0-2     -2
y= ax +b ==> 1=1.0+b ==> b= 1

b)M(-3,1) e N(2,-5),                  
   y = -6/5x - 13/5     decrescente
a= -5-1 = - 6 ==> a= -6/5
     2-(-3)    5
y= ax +b ==> -5= (-6/5).2+b ==> -5=-12/5 +b
 -25= - 12 + 5b ==>5b=-25+12 ==> 5b=-13 ==> b=-13/5
 
c) P(-1,-2) e Q(5,2)

   y = 4/6x - 8/6     crewscente
a= 2-(-2) = 2+ 2 ==> a=4/6
     5-(-1)     5+1
y= ax +b ==> 2=4/6.5+b ==> 2= 20/6+b
  12=20+6b ==> 6b= 12-20 ==> 6b=-8 ==> b = -8/6

d) R(3,4) e T(-6,8),
   y = -4/9.x + 48/9      decrescente
a= 8-4 = 4 ==> a= - 4
     -6-3  -9               9
y= ax +b ==> 4=-4/9.3+b ==> 4 = - 12/9 +b
  36 = -12 + 9b ==> 36+12=9b ==> 9b=48==> b = 48/9

e(S(5,-2) e Z(-6,-2)

   y = 0.x -2   ou y = - 2      constante
a= -2-(-2) = - 2+2 ==> a=  0  ==> a= 0 
     -6-5          -11             -11
y= ax +b ==> -2=0.5+b ==> b= - 2