In the xy plane line m is the reflection of line l across the x axis if the intersection of lines l and m is point r s why does s equal 0?

Say that line m is described by the function m(x) and line l by l(x). If m is a reflection of l in the x axis, then it follows that m(x) = -l(x). Try drawing a sketch to satisfy yourself of this. At the intersection(s) of l and m, m(x) = l(x). But we have also stated that m(x) = -l(x). This can only be true if the value of both functions (i.e. the y coordinate, s) is zero.