Explain the difference between the slopes of two parallel lines and the slope of two perpendicular lines.
parallel lines have the same slope
perpendicular lines in two dimensions have negative inverse slopes
slope b = -1/slope a
The slope of a line is a measure of how steep the line is. It describes the rate at which the line increases or decreases as we move along it.
Two lines are said to be parallel if they never intersect, meaning they do not cross each other at any point. When two lines are parallel, they have the same slope. In other words, the rate of increase or decrease is the same for both lines. To find the slope of a line, you need two points on the line. You can then calculate the difference in the y-coordinates and the difference in the x-coordinates between the two points. The slope is defined as the ratio of the change in the y-coordinates to the change in the x-coordinates.
On the other hand, two lines are said to be perpendicular if they intersect at a right angle, forming a 90-degree angle. The slopes of perpendicular lines are negative reciprocals of each other. In other words, if the slope of one line is m, then the slope of the perpendicular line is -1/m. To find the slope of a line, you again need two points on the line. Once you have the slope, you can find the negative reciprocal by taking its multiplicative inverse and changing the sign.
So, the key difference is that the slopes of parallel lines are equal, while the slopes of perpendicular lines are negative reciprocals of each other. To determine whether two lines are parallel or perpendicular, you can compare their slopes.