The equation of straight line passing through the point (1, -2) and pa

1.	The equation of straight line passing through the point (1, -2) and parallel to the line y = 5x - 2 is1. \(\rm (y + 2) = 5 (x +1)\)2. \(\rm (y + 2) = 5 (x -1)\)3. \(\rm (y + 2) = \frac 1 5 (x -1)\)4. None of these
Answer» 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 ⇒ \(\rm (y + 2) = 5 (x -1)\)

The equation of straight line passing through the point (1, -2) and parallel to the line y = 5x - 2 is1. \(\rm (y + 2) = 5 (x +1)\)2. \(\rm (y + 2) = 5 (x -1)\)3. \(\rm (y + 2) = \frac 1 5 (x -1)\)4. None of these

Answer» 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

⇒ \(\rm (y + 2) = 5 (x -1)\)