Question

Write an equation for the line that is parallel to the given line and that passes through the given point.

y = –5x + 3; (–6, 3)

(A) y = –5x + 9

(B) y = –5x + 27

(C) y = –5x – 27

(D) y = 5x – 9

Answer 1

You have to reject the "easily provable" wrong answers.
Start by looking at which equations are not even parallel to the line under question (the slope of a line is given by the number in front of x): the line we want must have the same slope (-5) for it to be parallel to the given line. So we exclude (D) since it has a slope of +5. After that we need to take every equation separately and input the point (-6, 3) (where x we input -6 and where y we input 3) and see if the equation holds or not (If it holds it means that that line passes through that point):
For (A) we get 3 = (-5 * -6) + 9 = 39 DOESN'T HOLD
For (B) we get 3 = (-5 * -6) + 27 = 57 DOESN'T HOLD
For (C) we get 3 = (-5 * -6) - 27 = 3 HOLDS

So the correct answer is (C)
Take care :)

Answer 2

y − y 1 = m(x − x1).
y - 3 = -5(x - x1).
y - 3 = -5(x - (-6)).
y - 3 = -5x - 30.
(C) y = -5x - 27.