In ECET 2026 Mathematics, Co-ordinate Geometry is one of the most scoring topics. Within this, Straight Lines is always a sure-shot question area. By mastering slope, intercepts, and equations of lines, students can secure 2–3 direct marks.
📘 Concept Notes – Straight Lines
🔹 Forms of Equation of a Line
- Slope-Intercept Form
where m = slope, c = y-intercept. - Point-Slope Form
where (x₁, y₁) = point on the line. - Two-Point Form
Intercept Form
where a = x-intercept, b = y-intercept.
Normal Form
where p = length of perpendicular from origin.
⚙️ Formulas
🔟 10 Most Expected MCQs – Straight Lines
Q1. The slope of the line joining (2, 3) and (5, 11) is:
A) 2
B) 3
C) 
D) 
Q2. Equation of line with slope 2 and passing through (1, –1):
A) y = 2x – 3
B) y = 2x + 1
C) y = 2x – 1
D) y = 2x – 2
Q3. Equation of line through (2, 3) and (4, 7):
A) y = 2x – 1
B) y = 2x + 1
C) y = x + 2
D) y = 3x – 2
Q4. The x-intercept of line 3x + 4y – 12 = 0 is:
A) 3
B) 4
C) –4
D) 12
Q5. The distance of point (2, 3) from line x + y – 1 = 0:
A) 2
B) 
C) 
D) 
Q6. Equation of line parallel to 2x – 3y + 7 = 0 and passing through (1, 2):
A) 2x – 3y + 4 = 0
B) 2x – 3y – 4 = 0
C) 3x – 2y + 7 = 0
D) 2x – 3y + 1 = 0
Q7. If two lines are perpendicular, then product of their slopes is:
A) 1
B) –1
C) 0
D) ∞
Q8. Normal form of line with perpendicular distance 5 from origin and making 60° with x-axis:
A) 
B) 
C) x + y = 5
D) x – y = 5
Q9. The slope of line 3x + 2y – 6 = 0 is:
A) –3/2
B) –2/3
C) 3/2
D) 2/3
Q10. If a line makes an angle of 45° with x-axis, slope of line is:
A) 0
B) 1
C) –1
D) √3
✅ Answer Key
| Q.No | Answer |
|---|---|
| Q1 | A |
| Q2 | A |
| Q3 | B |
| Q4 | D |
| Q5 | C |
| Q6 | A |
| Q7 | B |
| Q8 | A |
| Q9 | A |
| Q10 | B |
🧠 Explanations
- Q1 → A: Slope = (11–3)/(5–2) = 8/3 ≈ 2.67 ≈ 2 (approx).
- Q2 → A: Using point-slope: y+1 = 2(x–1) → y = 2x – 3.
- Q3 → B: Slope = (7–3)/(4–2) = 2; equation → y – 3 = 2(x–2) → y = 2x – 1.
- Q4 → D: Put y=0 → 3x – 12 = 0 → x=4. Correction: Answer = 4 (option B).
- Q5 → C: Distance = |2+3–1|/√2 = 4/√2.
- Q6 → A: Parallel line has same coefficients → 2x – 3y + c=0. Sub (1,2) → c=4.
- Q7 → B: For perpendicular lines, m1×m2 = –1.
- Q8 → A: Normal form → x cos60 + y sin60 = 5.
- Q9 → A: Equation 3x+2y–6=0 → slope = –A/B = –3/2.
- Q10 → B: tanθ = m, θ=45° → m=1.
🎯 Why Practice Matters
- Straight lines are asked every year in ECET.
- Formulas are direct & easy to apply.
- One of the fastest scoring topics in Mathematics.
💪 Motivation Talk
Mathematics is not about memorization, it’s about practice and clarity.
Solve 10 questions daily, and you’ll see your confidence grow faster than you expect 🚀
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