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IPMAT Indore Straight Lines — practice questions

Explore 14 free Straight Lines questions in IPMAT Indore Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Straight Lines questions and exercises with answers

Showing questions 1–14 of 14.

The slope of the line passing through the points (x₁, y₁) and (x₂, y₂) (where x₁ ≠ x₂) isRead the answer and worked solution →The slope of a horizontal line isRead the answer and worked solution →The equation of a line passing through the origin with slope m isRead the answer and worked solution →Two lines with slopes m₁ and m₂ are PARALLEL if and only ifRead the answer and worked solution →Two lines with slopes m₁ and m₂ are PERPENDICULAR ifRead the answer and worked solution →The slope of the line joining (2, 3) and (5, 11) isRead the answer and worked solution →The slope-intercept form y = mx + c of the line 3x + 4y = 8 gives a slope ofRead the answer and worked solution →The equation of the line passing through (2, −1) with slope 3 isRead the answer and worked solution →Equation of the line passing through (3, 4) and parallel to the line 2x − 3y = 5 isRead the answer and worked solution →The distance from the point (0, 0) to the line 3x + 4y − 25 = 0 isRead the answer and worked solution →The angle θ between two lines with slopes m₁ and m₂ satisfiesRead the answer and worked solution →The distance between the parallel lines 3x + 4y = 7 and 3x + 4y = 12 isRead the answer and worked solution →The intercept form of the equation of a line making intercepts a and b on the x- and y-axes isRead the answer and worked solution →The line 3x − 4y + 12 = 0 cuts the y-axis atRead the answer and worked solution →

Worked practice questions

The slope of the line passing through the points (x₁, y₁) and (x₂, y₂) (where x₁ ≠ x₂) is

  1. (y₂ − y₁) / (x₂ − x₁)
  2. (y₂ + y₁) / (x₂ + x₁)
  3. (x₂ + x₁) / (y₂ − y₁)
  4. (x₂ − x₁) / (y₂ − y₁)
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Correct answer: A. (y₂ − y₁) / (x₂ − x₁)

Slope m = (y₂ − y₁)/(x₂ − x₁) = rise/run. Vertical lines (x₁ = x₂) have undefined slope.

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The slope of a horizontal line is

  1. 0
  2. 1
  3. Undefined / infinite
  4. −1
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Correct answer: A. 0

A horizontal line has y₂ = y₁, so the numerator (y₂ − y₁) = 0, giving slope 0. Vertical lines have an undefined slope.

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The equation of a line passing through the origin with slope m is

  1. y = x / m
  2. y − x = m
  3. y = mx
  4. y = m + x
Show answer and solution

Correct answer: C. y = mx

Through the origin (0, 0) with slope m: y − 0 = m(x − 0) ⇒ y = mx.

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