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Question
Form the differential equation of all lines which makes intercept 3 on x-axis.
Solution
Equation of straight line is y = mx + c
At x-axis, y = 0
So, x = `(-c)/m`
Here, slope = m
If slope and x-intercept are equal
`(-c)/m = m`
⇒ c = – m2
∴ y = mx – m2
∴ `(dy)/(dx)` = m
Since, m = 3
∴ `(dy)/(dx)` = 3, which is the required equation.
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