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Parallel Line Equation:
where \( m \) remains the same and \( b_{\text{new}} \) is determined by the given point
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Parallel lines are lines in a plane that never meet; they are always the same distance apart. Two lines are parallel if they have the same slope but different y-intercepts.
The calculator uses the slope-intercept form of a line equation:
Where:
For parallel lines: The slope remains the same, and the new y-intercept is calculated using the given point \((x, y)\): \[ b_{\text{new}} = y - m \times x \]
Details: Parallel lines are fundamental in geometry and have applications in various fields including architecture, engineering, and computer graphics. Understanding how to find parallel lines is essential for solving many geometric problems.
Tips: Enter the slope (m) and y-intercept (b) of the original line, then enter the coordinates (x,y) of the point the parallel line should pass through. The calculator will provide the equation of the parallel line.
Q1: What makes two lines parallel?
A: Two lines are parallel if and only if they have the same slope but different y-intercepts.
Q2: Can vertical lines be parallel?
A: Yes, all vertical lines are parallel to each other since they all have an undefined slope.
Q3: How do I know if two equations represent parallel lines?
A: Compare their slopes - if the slopes are equal and the y-intercepts are different, the lines are parallel.
Q4: Can parallel lines ever intersect?
A: In Euclidean geometry, parallel lines never intersect. In other geometries (like projective geometry), parallel lines may intersect at infinity.
Q5: What's the difference between parallel and perpendicular lines?
A: Parallel lines have the same slope, while perpendicular lines have slopes that are negative reciprocals of each other.