Answer:
The correct option is <u>A) y - 1 = -4(x-2)</u> is an equation of the line going through (3, -6) and (1,2)
Step-by-step explanation:
we have to find which is not an equation of the line going through (3, -6) and (1,2)
Put   (3, -6) and (1,2) in Part A)
y - 1 = -4(x-2)
for (3, -6)
-6 - 1 = -4(3-2)
-7 ≠ -4
for (1,2)
2 - 1 = -4(1-2)
     1 = -4(-1)
      1 ≠ 4
This is not an equation of the line going through (3, -6) and (1,2)
Put   (3, -6) and (1,2) in Part B)
y - 2 = -4(x-1)
for (3, -6)
-6 - 2 = -4(3-1)
-8 = -8
for (1,2)
2 - 2 = -4(1-1)
     0= 0
This is an equation of the line going through (3, -6) and (1,2)
    
Put   (3, -6) and (1,2) in Part C)
y + 6 = -4(x-3)
for (3, -6)
-6 + 6 = -4(3-3)
        0 = 0
for (1,2)
2 + 6 = -4(1-3)
     8= 8
This is an equation of the line going through (3, -6) and (1,2)
    
Put   (3, -6) and (1,2) in Part D)
y  = -4x + 6
for (3, -6)
-6  = -4(3) + 6
        -6 = -6
for (1,2)
2  = -4(1) + 6
  2 = 2
This is an equation of the line going through (3, -6) and (1,2)
Hence, The correct option is <u>A) y - 1 = -4(x-2)</u> is an equation of the line going through (3, -6) and (1,2)