Parallel Line Calculator
Find the equation of a line parallel to a given line passing through a specific point
Calculate Parallel Line
Original Line Definition
Point the Parallel Line Passes Through
Line Equations and Properties
Original Line
Slope-Intercept Form:
y = 1x +0
Standard Form:
1x - y +0 = 0
Slope: 1.0000
Parallel Line
Slope-Intercept Form:
y = 1x +0
Standard Form:
1x - y +0 = 0
Slope: 1.0000
Passes through: (0, 0)
Distance Between Lines
0.0000 units
Formula: d = |b₂ - b₁| / √(m² + 1)
Note: The specified point lies on the original line. The parallel line will be identical to the original line (distance = 0).
Step-by-Step Solution
1. Identify the slope of the original line
Original line: y = 1x +0
Slope (m) = 1.0000
2. Use the same slope for the parallel line
Parallel lines have identical slopes.
Parallel line slope = 1.0000
3. Find the y-intercept using the given point
Point: (0, 0)
Using y = mx + b: 0 = 1.0000 × 0 + b
b = 0 - 1.0000 × 0 = 0.0000
4. Write the equation of the parallel line
Parallel line: y = 1x +0
5. Calculate the distance between the lines
Distance formula: d = |b₂ - b₁| / √(m² + 1)
d = |0.0000 - (0.0000)| / √(1.0000² + 1)
d = 0.0000 units
Example Calculation
Find Parallel Line
Given line: y = 3x - 5
Point: (1, 6)
Step 1: Slope = 3
Step 2: Same slope for parallel line
Step 3: 6 = 3(1) + b → b = 3
Parallel line: y = 3x + 3
Distance: |3 - (-5)| / √(3² + 1) = 2.53
Parallel Lines Properties
Same Slope
Parallel lines have identical slopes
Never Intersect
Parallel lines never meet
Constant Distance
Distance between parallel lines is constant
Different Y-Intercepts
Unless they are the same line
Calculator Tips
Use slope-intercept form for easiest input
Two points method works for any line
Standard form useful for vertical lines
Check if point lies on original line
Understanding Parallel Lines
What are Parallel Lines?
Parallel lines are straight lines in the same plane that never intersect, no matter how far they are extended. They maintain a constant distance from each other and have the same slope.
Key Characteristics
- •Identical slopes: Both lines have the same rate of change
- •Different y-intercepts: They cross the y-axis at different points
- •Constant separation: The distance between them never changes
- •No intersection: They never meet at any point
Mathematical Formulas
Parallel Line Equation
y = mx + b
Where m is the same as the original line's slope
Y-Intercept Formula
b = y₀ - mx₀
Using point (x₀, y₀) that the line passes through
Distance Between Lines
d = |b₂ - b₁| / √(m² + 1)
Distance between y = mx + b₁ and y = mx + b₂
Real-World Examples
Transportation
Railway tracks, highway lanes, airport runways
Architecture
Building facades, floor tiles, window frames
Sports
Football field lines, tennis court boundaries