If I am given a line, how do I find a line that is parallel to it? What about perpendicular?

The key fact here is to remember the relationship between the gradients of lines which are parallel and perpendicular. Two lines that are parallel will always have the same gradient. So if we have a line y = mx + c and another line y = nx + d then we know that the respective gradients, m and n, must be the same for them to be parallel lines.For two perpendicular lines, we need the gradients m and n to satisfy the relationship m*n = -1. This can be rewritten as n = -1/m. So if we are given a line y = mx+c, and we know m. Then using this we can find what n should be.Usually in a question, the constants c and d will be given to us, or we will be asked to find them given we know a point on the line.