UPSC NDA Math Model Paper 9

The equation of straight line passing through the point (x1,y1) is given by,(y−y1)=m(x−x1), where m is slope of the line.
The equation of straight line passing through the point (1,−2) is given by,
(y+2)=m(x−1) ....(1)
The equation of straight line passing through the point (1, -2) and parallel to the line y = 5x - 2
⇒ Slope of the line y = 5x - 2 is m = 5.
The slope of the parallel lines are equal.
So slope of the required line is m = 5
Equation (1) becomes
⇒ (y + 2) = 5(x − 1)