how can you determine if two lines are perpendicular
To determine if two lines are perpendicular, you need to check if their slopes are negative reciprocals of each other. Here's how you can determine if two lines are perpendicular:
1. Make sure the equations of both lines are in slope-intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.
2. Find the slopes of the two lines. The slope of a line is given by the coefficient of x in the equation y = mx + b.
3. Calculate the negative reciprocal of one of the slopes. To get the negative reciprocal of a slope, take its reciprocal (flip the fraction) and change the sign (from positive to negative or vice versa).
4. Compare the two slopes. If the slopes are negative reciprocals of each other, then the lines are perpendicular. If the product of the slopes is -1, they are perpendicular.
5. If the slopes are not negative reciprocals of each other, the lines are not perpendicular.
Remember, two lines that are vertical and horizontal are also considered perpendicular, with a slope of infinity and zero, respectively.