linear equations parallel to each other have same slope. what about perpendicular lines??
perpendicular lines have slopes that are the negative reciprocal of each other.
oh, i remember now, thanks
Perpendicular lines have slopes that are negative reciprocals of each other. Let's explore how to determine if two lines are perpendicular.
To find the slope of a line, we use the formula:
slope = (change in y-coordinates) / (change in x-coordinates)
Suppose we have two lines with equations y = m1x + b1 and y = m2x + b2, where m1 and m2 are the slopes of the respective lines.
For the lines to be perpendicular, the equation m1 * m2 = -1 must hold. In other words, the product of the slopes of two perpendicular lines will be -1.
To determine if two lines are perpendicular, calculate the slopes of both lines and check if their product is -1.
Here's an example:
Line 1 equation: y = 2x + 3 (slope = 2)
Line 2 equation: y = (-1/2)x + 5 (slope = -1/2)
To check if these lines are perpendicular, we multiply their slopes:
(2) * (-1/2) = -1
Since the product of the slopes is -1, we can conclude that Line 1 and Line 2 are perpendicular.
Therefore, if the product of the slopes of two lines is -1, they are perpendicular to each other.