Find parametric equations for the line through point P(-1,-1,-1) and Q(-5,7,3) A. x = t + 4; y = t - 8; z = -1t - 4 B. x = -4t - 1; y = 8t - 1; z = 4t - 1
C. x = -4t + 1; y = 8t + 1; z = 4t + 1
D. x = t - 4; y = t + 8; z = -t + 4

B) x = -4t - 1; y = 8t - 1; z = 4t - 1

Step-by-step explanation:

Explanation:-

Given points are   P(-1,-1,-1) and Q(-5,7,3)

Let (x₁ , y₁ , z₁) =  P(-1,-1,-1)

Let (x₂ , y₂ , z₂) =   Q(-5,7,3)  

Parametric equation of the line passing through the points  (x₁ , y₁ , z₁) and      (x₂ , y₂ , z₂)

Equating  each term

     ⇒  x + 1 = - 4 t

    ⇒   x = - 4 t -1

         y + 1 = 8 t

     ⇒  y  = 8 t - 1

  ⇒  z +1 = 4t

   ⇒ z = 4t -1

Final answer:-

parametric equations for the line through point P(-1,-1,-1) and Q(-5,7,3)

are

x = -4t - 1; y = 8t - 1; z = 4t - 1

  the correct choice is marked

step-by-step explanation:

the first two graphs show multiple turning points. the last graphs matches the description in every detail.