Post your 50 or more word response to the following in the assignment link:
How can you determine if two lines are perpendicular?
Your response should include the following:
· How the slopes of two perpendicular lines relate;
· How you recognize if two lines are perpendicular on a graph;
· How you recognize if two lines are perpendicular simply from their equations.
To determine if two lines are perpendicular, you need to consider their slopes. Perpendicular lines have slopes that are negative reciprocals of each other. In other words, if the slope of one line is m, the slope of the other line is -1/m.
If you have the equations of two lines, you can determine if they are perpendicular by comparing their slopes. For example, if the equation of one line is y = 3x + 2, and the equation of the other line is y = -1/3x + 4, you can see that the slopes are opposite reciprocals of each other (3 and -1/3). Hence, the lines are perpendicular.
On a graph, you can visually recognize if two lines are perpendicular by observing their orientation. Perpendicular lines intersect at a right angle, forming a 90-degree angle. If the lines intersect and their angles are congruent, then they are perpendicular. You can also notice this by checking the slopes – they should be negative reciprocals.
In summary, to determine if two lines are perpendicular, you need to check if their slopes are negative reciprocals of each other. This can be done by analyzing their equations or visually inspecting their orientation on a graph.