Question

Find the equation of the line passing through the point of intersection of lines 2x+y = 5 and x-2y = 5 and having y-intercept equal to -3/7​

Answer 1

Answer:

The point of intersection of given lines is (2,1). To get an equation of a line, which is at a minimum distance from (1,2) , we need to recognize the fact that required line will be perpendicular to line joining these 2 points. This is because the least distance between a line and a point is the length of perpendicular from the point to the line.

Slope of perpendicular = 2−11−2=1−1=−1

Slope of required line = 1 , because product of slopes of perpendicular lines is (−1).

So, required equation is (y−1)=1(x−2).

(This is in slope-point form, can be simplified easily.)