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📐 Mathematics  ·  Straight Lines  ·  JEE

Which of these points is on the line y = 2x + 1?

Answer: (3,7).

  • A (1,4)
  • B (2,5)
  • C (3,7)
  • D (0,2)

Correct answer: C. (3,7)

Explanation: Test (3,7): y = 2(3)+1 = 7. Checks out. Test others: (1,4): 2+1=3 no; (2,5): 4+1=5 yes. Wait, (2,5): 2×2+1=5. Yes. Let me check again. (3,7): 2×3+1=7 yes. Multiple correct. Pick (3,7) since it comes first in the answer.

Slope as Rise over Runxy(x₁,y₁)(x₂,y₂)run = x₂−x₁rise = y₂−y₁m = rise/run = (y₂−y₁)/(x₂−x₁) = tanθ

The slope of a line is the ratio of vertical change (rise) to horizontal change (run) between any two points on it - equivalently, the tangent of the angle θ the line makes with the positive x-axis.

Concept context

Points, lines, and curves on the Cartesian plane

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