# Find the point on the line y = 5x + 2 that is closest to the origin.

Linear equations and graphs

Find the point on the line $$y = 5x + 2$$ that is closest to the origin.

2021-06-13
let the point be $$(x,5x+2)$$
We have to minimize
$$d = x^2 + (5x+2)^2$$
$$d' = 2x+ 10(5x+2) = 0$$
$$52x = -20$$
$$x=-\frac{10}{26} =-\frac{5}{13}$$
$$y = \frac{1}{13}$$
$$(-\frac{5}{13} , \frac{1}{13})$$