Parallel Line Through a Point Calculator

Two lines are parallel when they have the same slope (m) but different y-intercepts. They never intersect and remain the same distance apart at every point. For example, y = 2x + 3 and y = 2x + 7 are parallel because both have a slope of 2.

First, identify the slope of the reference line. Since parallel lines share the same slope, your new line has the same m. Then substitute the given point (x₁, y₁) into y - y₁ = m(x - x₁) and simplify to slope-intercept form y = mx + b, solving for b.

When a line is written as Ax + By = C, its slope is m = -A/B (assuming B ≠ 0). Rearranging to slope-intercept form gives y = (-A/B)x + (C/B). A parallel line will have the same slope -A/B.

A line is considered parallel to itself in a trivial sense, but in standard geometry, parallel lines are distinct — they have the same slope but different y-intercepts. If a point lies on the original line, the 'parallel' line through that point is the original line itself.

Parallel lines have the same slope (m₁ = m₂) and never intersect. Perpendicular lines intersect at a right angle (90°), and their slopes are negative reciprocals of each other: m₁ × m₂ = -1. For instance, if one line has slope 3, a perpendicular line has slope -1/3.

No — parallel lines share the same slope but have different y-intercepts (unless the given point lies on the original line). The y-intercept of the parallel line is determined by plugging the given point coordinates into the line equation and solving for b.

If B = 0, the line is vertical (x = C/A) and has an undefined slope. A line parallel to a vertical line is also vertical, passing through the given point as x = x₁. This calculator assumes B ≠ 0 for the standard form calculation.

Yes — this calculator accepts lines in both slope-intercept form (y = mx + b) and standard form (Ax + By = C). Simply select your preferred input format, enter the coefficients, and provide the point coordinates to get the parallel line equation in both forms.