How can I tell if two lines are perpendicular from the equations?

In order to compare two equations they need to be in the same form. This means that the y's have to be on the left, and the x's have to be on the right - so the first step is to rearrange both of the equations that you are comparing to be in this form: y = mx + c where m is a number, and c is a number.

When we are talking about perpendicular lines, we really don't care about the c value as all this does is move the lines upwards and downwards along the y axis - what is important is m, the gradient value. Because we have two equations, we have two values of m to look at: m1, and m2. If the lines are perpendicular, then m1 will be the negative reciprocal of m2 - what does that mean?! Simply, that m1 = -1/m2. - Or even more simply, that if we multiply m1 by m2, the answer will be -1. 

In summary: rearrange, and then multiply the m values to check if the answer is -1.