A straight line passes through the point \(( 2,0 )\) and has gradient \(m\). Write down the equation of the line.
Find the two values of \(m\) for which the line is a tangent to the curve \(y = x ^ { 2 } - 4 x + 5\). For each value of \(m\), find the coordinates of the point where the line touches the curve.
Express \(x ^ { 2 } - 4 x + 5\) in the form \(( x + a ) ^ { 2 } + b\) and hence, or otherwise, write down the coordinates of the minimum point on the curve.