9. Which of the following lines is parallel to 2x + y =7 and passes through (4, 1)?

Step-by-step explanation:

Let 2x + y = 7   be [a]  &  [a] ║ [b]

Since [a] ║ [b], the the gradient (m) of both [a] and [b] are equal ( -2).

The gradient is -2, since 2x + y = 7 ≡ y = -2x + 7

Now, by using the point slope form (y - y₁) = m (x - x₁); where (x₁ , y₁) = (4 , 1)

⇒   [b]   →  (y - 1) = -2 (x - 4)

            →   y - 1 = 8 - 2x

The diagram below is a graph created with Desmos which confirms the answer.