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Maths Straight Line Slope of Line, Equation of Line in Different Forms, Gradient of A Line, Straight Line Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

For how many integral values of m do the lines y + mx – 1

= 0 and 3x + 4y = 9 intersect in points having integral

coordinates –

Infinite

Text Solution

Verified by Experts

The correct answer is:

We have 3x + 4y = 9

i.e x = = 3 –

Thus, points lying on the above line and having integral coordinates are given by

P ≡ (3 – 4k, 3k) k ∈ I

If P also lies on y + mx – 1 = 0, then we have

3k + m (3 – 4k) – 1 = 0

gives m = , k ∈ I

For m to be an integer, we have

|4k – 3| ≤ |3k – 1|

i.e. – (3k – 1) ≤ (4k – 3) ≤ (3k – 1)

i.e. ≤ k ≤ 2

There are only two integral values of k lying in the above integral, viz. k = 1, 2, Hence, there are only two integral values of m.

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