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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 − y 1 = 2(x − x 1) And then put in the point (5,4): y − 4 = 2(x − 5) That is an answer!
- Slope
- −0.5
Hence, it can be said that if the slope of two lines is the same, they are identified as parallel lines, whereas, if the slope of two given lines are negative reciprocals of each other, they are identified as perpendicular lines. ☛ Related Articles. Check out the following pages related to parallel and perpendicular lines. Points and Lines
May 7, 2024 · Lines that intersect each other at right angles are known as perpendicular lines. Define Parallel Lines. Lines that are always the same distance apart and do not intersect are known as parallel lines. How are Parallel and Perpendicular Lines Similar? Parallel and perpendicular lines have one similarity is that they both are consist of straight ...
Definition of Parallel and Perpendicular Lines. Parallel and perpendicular lines play a vital role in geometry. Both of them have distinct properties and applications. Definition of Parallel Lines. Two lines are said to be parallel if they lie in the same plane and the distance between them is the same. Parallel lines never meet each other.
- 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.
The red line is perpendicular to the blue line: Here also: Learn more at perpendicular lines. Perpendicular to a Plane. A line is perpendicular to a plane when it extends directly away from it, like a pencil standing up on a table. If the pencil is perpendicular to a line on the table, then it might be perpendicular to the table: Or it might be ...
Likewise, parallel lines become perpendicular when one line is rotated 90°. Parallel Curves. Curves can also be parallel when they keep the same distance apart (called "equidistant"), like railroad tracks. The red curve is parallel to the blue curve in both these cases:
