How do you determine if two lines are perpendicular?
The slopes are negative reciprocals of each other.
For instance, if one has the slope of 8, the other must have a slope of -1/8
To determine if two lines are perpendicular, you can use the concept of slope. Perpendicular lines have slopes that are negative reciprocals of each other. Here's how you can determine if two lines are perpendicular:
1. Obtain the equations of the two lines in the form y = mx + b, where m is the slope and b is the y-intercept.
2. Calculate the slopes of the two lines. The slope of a line is given by the coefficient of x in the equation. For example, if Line 1 has an equation y = 2x + 3, the slope of Line 1 is 2.
3. Find the negative reciprocal of the slopes you calculated in step 2. The negative reciprocal is found by taking the reciprocal (flipping the fraction upside down) and changing the sign. For example, if the slope of Line 1 is 2, its negative reciprocal is -1/2.
4. Compare the slopes of the two lines. If the slopes of Line 1 and Line 2 are negative reciprocals of each other, then the lines are perpendicular. For example, if the slope of Line 2 is -1/2, and Line 1 has a slope of 2, then the two lines are perpendicular.
By following these steps, you can determine if two lines are perpendicular by comparing their slopes.