Which of the following lines is not perpendicular to y=2x+1? (A) y+1/2x=6 (B) 2y=4-x (C) 2x+y=4 (D) y=-1/2(7+x)

First of all, we need to figure out how to tell whether 2 lines are perpendicular. For any equation written in the form 'y=mx+c', the important bit of information we need to answer this question is the value of 'm', or the gradient of each line. If 2 lines are perpendicular, then both of their gradients multiplied together will be equal to -1 (m1m2=-1). It is easier to explain this by jumping into the question above and using a real example. Looking at the question, the equation we are first given is 'y=2x+1'. The important bit of info we need to focus on is the coefficient of 'x', which in this case is 2. If we use the equation 'm1m2=-1', then we get '2*m2=-1', where 'm2' is the gradient of the line we are looking for. By a simple rearrangement, we get 'm2=-1/2'. Now all we need is to go back to the question and see which of the 4 options does NOT have a gradient of '-1/2', as the question states. The easiest way to achieve this is to rearrange all of the answers into the form of 'y=mx+c', or making 'y' the subject of each. (A) becomes y=-1/2x+6 which has a gradient of -1/2(B) becomes y=-1/2x+2 which also has a gradient of -1/2(C) becomes y=-2x+4 which has a gradient of 2 and is therefore not perpendicular to the equation in the question Just to double check though: (D) becomes y=-1/2x+7/3 which also has a gradient of -1/2 This means that the answer to the question is (C)