Correct Answer – Option 2 : \(\rm (y + 2) = 5 (x -1)\)

Concept:

The equation of the straight line passing through the point \(\rm (x_1, y_1)\) is given by, 

\(\rm (y – y_1) = m (x -x_1)\), where m is the slope of the line.

Note: The slope of the parallel lines are equal

Calculations:

The equation of straight line passing through the point \(\rm (x_1, y_1)\) is given by, 

\(\rm (y – y_1) = m (x -x_1)\), where m is slope of the line.

The equation of straight line passing through the point (1, -2) is given by, 

\(\rm (y + 2) = m (x -1)\)          ….(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

⇒ \(\rm (y + 2) = 5 (x -1)\)