Correct Answer - Option 3 : -3
Concept:
The general equation of a line is y = mx + c
Where m is the slope and c is any constant
1. The slope of parallel lines is equal.
2. Slope of the perpendicular line have their product = -1
The equation of a line passing through (x1, y1) and (x2, y2) is:
\(\rm {y-y_1\over x-x_1}={y_2-y_1\over x_2-x_1}\)
Calculation:
The line passing through the points (2, -1) and (1, 2)
The equation of the line is
\(\rm {y-2\over x-1}={-1-2\over2-1}\)
y - 2 = -3x + 3
y = -3x + 5
⇒ Slope(m1) = -3 and c1 = 5
Now for the slope of the parallel line (m2)
m1 = m2
⇒ m2 = -3
