Hello,Welcome to StudentBro.
Hello,Welcome to StudentBro.
Hello,Welcome to StudentBro.
Straight lines are a fundamental chapter in JEE Maths, forming the base of coordinate geometry. The study of straight lines involves understanding slopes, equations, intercepts, parallelism, perpendicularity, and intersections. Mastering straight lines is essential for solving JEE Main and Advanced coordinate geometry problems efficiently. At StudentBro.in, we provide a comprehensive guide covering formulas, properties, examples, and practice problems to help JEE aspirants excel in straight lines.
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A straight line in a plane is a set of points that extends infinitely in both directions, maintaining a constant slope.
Standard representation: y = mx + c
m = slope of the line
c = y-intercept
Example: Line y = 2x + 3 has slope 2 and y-intercept 3.
The slope (m) measures the steepness of a line and is calculated as:
m = (y₂ - y₁) / (x₂ - x₁)
Positive slope: line rises from left to right
Negative slope: line falls from left to right
Zero slope: horizontal line
Undefined slope: vertical line
Example: Slope of line joining points (1, 2) and (3, 6) → m = (6-2)/(3-1) = 2
1. Slope-Intercept Form: y = mx + c
m = slope
c = y-intercept
2. Point-Slope Form: y - y₁ = m(x - x₁)
Passes through point (x₁, y₁) with slope m
3. Two-Point Form: (y - y₁)/(y₂ - y₁) = (x - x₁)/(x₂ - x₁)
Passes through two points (x₁, y₁) and (x₂, y₂)
4. General Form: Ax + By + C = 0
Example: Line passing through (2, 3) with slope 2 → y - 3 = 2(x - 2) → y = 2x - 1
x-intercept: Point where line crosses x-axis (y = 0) → x = -C/A
y-intercept: Point where line crosses y-axis (x = 0) → y = -C/B
Example: Line 2x + 3y - 6 = 0 → x-intercept = 3, y-intercept = 2
Parallel Lines: Same slope, different intercepts → m₁ = m₂
Perpendicular Lines: Product of slopes = -1 → m₁ × m₂ = -1
Example: Line y = 2x + 1 is parallel to y = 2x - 3, perpendicular to y = -1/2 x + 5
Line: Ax + By + C = 0, Point: P(x₁, y₁)
Distance = |Ax₁ + By₁ + C| / √(A² + B²)
Example: Distance of point (1, 2) from line 3x + 4y - 5 = 0 → |31 + 42 - 5| / √(9 +16) = 6/5
If slopes of two lines are m₁ and m₂, angle θ between them:
tan θ = |(m₁ - m₂) / (1 + m₁ m₂)|
θ = 0 → lines are parallel
θ = 90° → lines are perpendicular
Example: Slopes m₁ = 1, m₂ = -1 → tan θ = |(1+1)/(1-1)| → θ = 90°
Solve two line equations simultaneously to find intersection point
Applicable in triangles, polygons, and coordinate geometry problems
Example: Line1: y = x + 2, Line2: y = -x + 4 → Solve x + 2 = -x + 4 → x = 1 → y = 3 → Intersection (1, 3)
Find equations using slope, points, or intercepts
Solve parallel, perpendicular, and intersecting line problems
Determine distance of point from line
Find angles between lines
Solve coordinate geometry questions in JEE Main and Advanced
Memorize slope, distance, and equation formulas
Use slope properties for parallel and perpendicular lines
Solve problems using point-slope or two-point form for accuracy
Draw a diagram whenever possible to visualize
Practice previous year JEE straight line problems for speed
At StudentBro.in, students can access:
Step-by-step explanations for equations, slopes, intercepts, parallel and perpendicular lines
Worked examples for intersection and angle problems
Practice questions with solutions and shortcuts
Tips for quick problem-solving and exam strategy
Revision notes for last-minute preparation
Find the slope of line joining points (2, 3) and (5, 7)
Find the equation of a line passing through (1, 2) with slope 3
Find x and y intercepts of line 2x + 3y - 6 = 0
Determine if lines y = 2x + 3 and y = 2x - 1 are parallel
Find distance of point (3, 4) from line x + 2y - 5 = 0
Regular practice improves accuracy, speed, and confidence in solving straight line problems in JEE exams.
Straight Lines are a vital chapter in JEE Maths. Understanding slope, intercept, equation forms, parallel and perpendicular lines, distance, and angle formulas allows students to solve coordinate geometry problems efficiently. At StudentBro.in, we provide a complete guide from basics to advanced problem-solving, making straight lines simple, practical, and exam-oriented.
Mastering this topic ensures students can tackle line equations, intersections, and geometric problems confidently in both JEE Main and Advanced exams.
