What is the equation in point-slope form for the line parallel to y = 4x – 14 that contains P(–2, –6)?A. y – 6 = 4(x + 2)B. x + 6 = –4(y + 2)C. y + 6 = 4(x + 2)D. y + 6 = –4(x + 2)

Point t slope form:
y + y value = m (x + x value) where m is the gradient
Parallel line must have the same gradient as the two lines never meet, so the gradient must be 4. This eliminates option B and D.
Remember that point-slope form is still an equation, so the values of both sides must be equal. So let's substitute the given coordinates.
Option A:
y-6=4(x+2)
-6-6 (-12) does not equal to 4(-2+2) (0)
Option C:
y+6=4(-2+2)
-6+6 (0) = 4(-2+2) (0)
Therefore, option C is your answer.