Maybe we can walk through this? At first glance, the first thing I would do is find the derivative of , but that's not right.
If you haven't learned "the whole dy/dx thing", why did you refer to finding the derivative in your first post? The formula you give is for the slope of a straight line. If f(x) is not linear, it is the slope of a "secant" line, a line that crosses the graph at x and x+y, not the tangent line. Since you don't yet know the derivative (I suspect this problem is preliminary to introducing the derivative), here's a method that predates the calculus:
If y= 5x+ 45 and meet at all, we must have or . Let u= so that . The equation becomes . If x= a at the point of intersection then x- a= must be a factor of that polynomia. If fact, to be tangent that must be a double factor- we must have Multiplying the right side, we get for all u. Comparing coefficients, and . Solve the second equation for a and use that to solve the first equation for k.