Angle relationships with Parallel Lines
It is important to know about their relationship to find a parallel line given a point. Lines on a plane that are parallel to one another do not intersect or meet at any point. They are always equidistant and parallel to one another. Non-intersecting lines are parallel lines. Parallel lines can also be said to meet at infinity.
Additionally, pairs of angles are created when a transversal meets two parallel lines, such as:
- Coordinating angles
- Modified interior angles
- Modified exterior angles
- Opposing vertical angles
- Linear couple
Two lines are said to intersect at a point in a plane and are referred to as intersecting lines. They are referred to as perpendicular lines if they intersect at an angle of 90 degrees.
How to Find a Parallel Line Given a Point from Equation
Understand the examples to find out the parallel lines of a given point. If you want to find it quickly without difficult and manual calculation. You can use online Parallel Line Calculator.
Examples are given below:
Example # 1:
Find the equation of the line that passes through the point (3, 5) (3, 5) and is parallel to the line y = 2x + 5y = 2x + 5.
y = 2x + 5y = 2x + 5 is the line’s equation in the slope-intercept form.
The parallel line has the same slope: m = 2m = 2.
The parallel line’s equation is therefore y = 2x + ay = 2x + a.
We utilize the knowledge that the line must pass through the specified point to determine as: 5 = (2) (3) + a.
As a result, a=11a=11.
Consequently, the line’s equation is y = 2x + 11y = 2x + 11.
Example # 2:
What line passes between (3, 2) and 2x + 3y = 6?
Determine the slope of the provided line: y = mx + b (slope intercept form)
Y = −2 / 3x+2 Consequently, the slope is 2/3.
Since parallel lines have the same slope, we must now use the point-slope formula to obtain the equation of a line passing through the points (3, 2) and having a slope of 23.
2 = −2 / 3(3) + b
So, b = 4
y = 2 / 3x + 4 is the revised equation as a result.
Related: How to Find Limiting Reactions?
What line passes between (3, 2) and 2x + 3y = 6?
Determine the slope of the provided line: y = mx + b (slope intercept form)
Y = −2 / 3x + 2 consequently, the slope is 2/3.
Since parallel lines have the same slope, we must now use the point-slope formula to obtain the equation of a line passing through the points (3, 2) and having a slope of 23.
2 = −2 / 3(3) + b
So, b = 4
y = 2 / 3x + 4 is the revised equation as a result.
We can easily understand the methods to find a parallel line given a point from these solved examples.
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FAQs
How do parallel lines work?
On a plane, parallel lines are those lines that never cross one another. They are lines that do not cross.
What characteristics do parallel lines have?
Parallel lines are always spaced equally from one another. They do not cross over one another. Parallel lines intersected by a transversal produce a pair of angles. As a result, comparable angles, alternate interior angles, alternate exterior angles, vertical angles, and the total of the interior angles on the same side of the transversal are supplementary angles are all identical.
