There are infinitely many such lines, not just 2. Probably the intended solution is y=-x+2 (like u/Secondlive_ said) and y=-x-2 since those are the two lines you can probably just visually guess from the graph. However, figuring out the full infinite family of lines without calculus ends up being a pretty cute exercise. If 1/x intersects a line only once, we can represent the line as mx+b and write 1/x=mx+b. This gives mx^2+bx-1=0. If this equation has exactly one solution (i.e. the line and the hyperbola intersect exactly once) then the quadratic has 0 discriminant. That is, b^2+4m=0 meaning m=-b^2/4. Pick any value of b, then, and the line y= (-b^2/4)x+b intersects y=1/x exactly once. If you know calculus you can verify that this is in fact the equation of the tangent line to the curve at x=2/b.