This is a straight line with the equation y = -(1/7)x + 10/7
The minimum distance from the origin to this line is provided by a straight line that passes through the origin and which is perpendicular to the straight line.
The slope of the perpendicular line is 7 because the product of the two slopes should be -1. The perpendicular line is of the form y = 7x + c.
Because the line passes through (0,0), therefore c = 0. The line y = 7x intercepts the original line when y = 7x = -(1/7)x + 10/7
Therefore 7x = -(1/7)x + 10/7 Multiply through by 7. 49x = -x + 10 50x = 10 x = 1/5 y = 7x = 7/5
The minimum distance is d = √(x² + y²) = √[(1/5)² + (7/5)²] = √2