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Find the equation of the line that is: parallel to y = 2x + 1. and passes though the point (5,4) The slope of y = 2x + 1 is 2. The parallel line needs to have the same slope of 2. We can solve it by using the "point-slope" equation of a line: y − y1 = 2 (x − x1) And then put in the point (5,4): y − 4 = 2 (x − 5)
- Slope
- −0.5
A General Note: Parallel and Perpendicular Lines. Two lines are parallel lines if they do not intersect. The slopes of the lines are the same. f (x) =m1x+b1 and g(x) =m2x+b2 are parallel if m1 = m2 f (x) = m 1 x + b 1 and g (x) = m 2 x + b 2 are parallel if m 1 = m 2. If and only if b1 = b2 b 1 = b 2 and m1 = m2 m 1 = m 2, we say the lines ...
May 7, 2024 · Perpendicular lines are intersecting lines, whereas parallel lines never intersect. Parallel lines in geometry are lines that never intersect and are always at the same distance from each other. On the other hand, perpendicular lines are lines that intersect each other at a right angle, forming a 90° angle.
- Both lines have a slope \(m=\frac{3}{4}\) and thus are parallel. Perpendicular lines are lines in the same plane that intersect at right angles (\(90\) degrees).
- Perpendicular lines have slopes that are opposite reciprocals, so remember to find the reciprocal and change the sign. In other words,
- Through the point \((6, −1)\) we found a parallel line, \(y=\frac{1}{2}x−4\), shown dashed. Notice that the slope is the same as the given line, but the \(y\)-intercept is different.
- It is not always the case that the given line is in slope-intercept form. Often you have to perform additional steps to determine the slope.
Answer: The first step is to write the equation in slope-intercept form. We see that the slope is m=\frac {5} {3} m = 35. This means that the slope of the line perpendicular to the given line is the negative reciprocal or -\frac {3} {5} −53. Next, we use point-slope form with this new slope and the given point.
Parallel lines are lines that never intersect, and they form the same angle when they cross another line. Perpendicular lines intersect at a 90-degree angle, forming a square corner. We can identify these lines using angles and symbols in diagrams. Created by Sal Khan and Monterey Institute for Technology and Education.
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Perpendicular lines are marked with "a box" to indicate the location of the right angle. Perpendicular lines intersect in one location, which becomes the vertex of the right angle. Remember that a right angle contains 90º (think of the angle in the corner of a square).
