True or False:
If a line \(L_1\) has the equation [tex] y = mx + b [/tex], where \(m\) and \(b\) are constants with \(m \neq 0\), then an equation of a line \(L_2\) perpendicular to \(L_1\) has the form [tex] y = -\frac{1}{m}x + C [/tex], where \(C\) is a constant.
Answer (2)
L 1 : y = m x + b L 2 : y = − m 1 × C L 1 ⊥ L 2 − F A L SE − − − − − − − − − − − − − − − − − − − − L 3 ⊥ L 1 ⟺ L 3 = − m 1 + C
The statement is True. The equation of a line L 2 that is perpendicular to line L 1 with slope m indeed has the form y = − m 1 x + C . This is because the slopes of perpendicular lines are negative reciprocals of each other.
;
