Why is slope of perpendicular lines?
Similarly, you may ask, what is the slope of a perpendicular line?
Correct answer: Therefore, the slope of the original line is 1/2. A line perpendicular to another has a slope that is the negative reciprocal of the slope of the other line. The negative reciprocal of the original line is –2, and is thus the slope of its perpendicular line.
Furthermore, is the slope of a perpendicular line opposite? It doesn't matter what the y-intercepts are, lines are perpendicular as long their slopes are opposite reciprocals of one another. Perpendicular lines have opposite reciprocal slopes. Both these lines have reciprocal slopes to the slope of 7 in the original equation, but only the first line is the opposite reciprocal.
Also, why are the slopes of perpendicular lines negative reciprocals?
In the coordinate plane, all vertical lines are parallel to the y-axis and all horizontal lines are parallel to the x-axis. These lines are perpendicular since their slopes are negative reciprocals. The negative reciprocal of 2 is . If you multiply a slope times its negative reciprocal, the result is always -1.
How do you prove that two lines are perpendicular using slope?
Two lines are perpendicular if and only if their slopes are negative reciprocals. To find the slope, we must put the equation into slope-intercept form, , where equals the slope of the line. We begin by subtracting from each side, giving us . Next, we subtract 32 from each side, giving us .