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Parallel Lines. How do we know when two lines are parallel? Their slopes are the same! The slope is the value m in the equation of a line: y = mx + b. Example: 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.
- Slope
- −0.5
Explanation: In order for two lines to be parellel, their slopes have to be the same. Find the slope of the line connecting those two points using the general slope formula, , where the points are and . In our case, the points are (–8,9) and (3,–4). The slope is calculated below.
In this article, we learned about the slope of parallel lines, how to find the slope of parallel lines, its derivation, and how to find equations of parallel lines. Let’s solve a few examples and practice problems.
- Two lines are parallel if both lines have equal slopes.
- Let three lines have slopes $m_1,\; m_2$, and $m_3$. Then the condition for three lines to be parallel to each other is $m_1 = m_2 = m_3$.
- Two lines with slopes $m_1$ and $m_2$ are perpendicular if $m_1= \;-\;\frac{1}{m_2}$ .
- If we have two parallel lines with slopes as $m_1$ and $m_2$, then the formula for the slope of parallel lines is $m_1 = m_2$.
- The angle between two parallel lines is either $0^\circ$ or $180^\circ$.
Free parallel line calculator - find the equation of a parallel line step-by-step.
The equation of a line from the slope of parallel lines can be calculated using the point-slope form or the slope-intercept form. The slope of a line is equal to the slope of parallel lines, and we have m 1 = m 2 .
Jan 16, 2024 · To figure out if 2 lines are parallel, compare their slopes. You can find the slope of a line by picking 2 points with XY coordinates, then put those coordinates into the formula Y2 minus Y1 divided by X2 minus X1. Calculate the slope of both lines. If they are the same, then the lines are parallel.
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Apr 18, 2020 · This step-by-step guide will teach you how to graph parallel lines and perpendicular lines using slope! The guide includes several examples of how to find the slopes of parallel and perpendicular lines (and how to graph them).
