are the lines perpendicular
When two lines are perpendicular, the slope of one is the negative reciprocal of the other. If the slope of one line is m, the slope of the other is. Try this Drag points C or D. Note the slopes when the lines are at right angles to each other. Slope: Parallel and Perpendicular Lines (page 2 of 2). Parallel lines and their slopes are easy. Since slope is a measure of the angle of a line from the horizontal, and since parallel lines must have the same angle, then parallel lines have the same slope — and lines with the same slope are parallel. In Fig 1, the line AB and a line segment CD appear to be at right angles to each other. Determine if this is true. To do this, we find the slope of each line and then check to see if one slope is the negative reciprocal of the other. If the lines are perpendicular, each will be the negative reciprocal of the other. In Fig 1, find a line through the point E that is perpendicular to CD. The point E is on the y-axis and so is the y-intercept of the desired line. Once we know the slope of the line, we can express it using its equation in slope-intercept form y=mx+b, where m is the slope and b is the y-intercept. Put this together with the sign change, and you get that the slope of the perpendicular line is the negative reciprocal of the slope of the original line — and two lines with slopes that are negative reciprocals of each other are perpendicular to each other. Parallel lines have the same slope and will never intersect. Parallel lines continue, literally, forever without touching (assuming that these lines are on the same plane). Parallel Lines in greater depth. On the other hand, the slope of perpendicular lines are the negative reciprocals of each other, and a pair of these lines intersects at 90 degrees. Perpendicular Lines in greater depth. Perpendicular lines are a bit more complicated. If you visualize a line with positive slope (so it's an increasing line), then the perpendicular line must have negative slope (because it will be a decreasing line). So perpendicular slopes have opposite signs. Example of perpendicular lines. As you can see from the picture below: 1  the slope of these lines are negative reciprocals. $$\ 2 frac{2}{3}$$ and $$-\frac{3}{2}$$ are negative reciprocals. 3  these lines are perpendicular and intersect at 90 degrees. If the slope of one line is m then the slope of the other line is the negative reciprocal of m, or. So for example in the figure above, the line AB has a slope of 0.5, meaning it goes up by a half for every one across. The line CD if it is perpendicular to AB has a slope of -1/0.5 or -2. Adjust points C or D to make CD perpendicular to AB and verify this result. Fig 1. Lines are still perpendicular. Remember that the equation works both ways, so it doesn't matter which line you start with. Let's find the equation of the line that passes through the point.
When two lines are perpendicular, the slope of one is the negative reciprocal of the other.