What point on the line y=5x+10 is closest to the origin?

Note that the coordinates of any points on the line can be written as (k, 5k+10) for some real number k.then let (m, 5m+10) be a point on the line.then the distance between the point and the origin is sqrt(m^2 + (5m+10)^2 ). we denote it by d.note that to find the minimum value of d, it is equivalent to find the minimum value of d^2, as d> 0. let d=d^2.differnetiate d with respect to m.we have dd/dm = 52m+100.set dd/dm=0, we have m=-25/13.note that the second derivative of d is 52, which is greater than 0.hence d is at minimum when m= -25/13.hence, the desired point is (-25/13, 5/13)