If a line L1 has equation y = mx + b, where m and b are constants with m ¹ 0,then an equation of a line L2 perpendicular to L1 has the form , where C is a constant.
L2: y = -1/m x + C
To find the equation of a line perpendicular to L1, we need to consider the properties of perpendicular lines. In particular, the slopes of perpendicular lines are negative reciprocals of each other.
The equation of L1 is given as y = mx + b, where m is the slope of L1. Perpendicular lines will have a slope that is the negative reciprocal of m, so let's call the slope of the perpendicular line L2 as -1/m.
To find L2's equation, we first need to determine its slope. So, the slope of L2 is -1/m.
Now, let's find the equation of L2. We know that the equation of a line can be written in the form y = mx + c, where c is a constant. Since we have the slope of L2 as -1/m, the equation becomes:
y = (-1/m)x + c
Therefore, the equation of a line L2 perpendicular to L1 has the form y = (-1/m)x + c, where c is a constant.