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The ordinate of a point P on the line 6x...

The ordinate of a point `P` on the line `6x + y = 9` which si closest to point `(-3, 1)` can be expressed in the form `a//b`. Where `a, b, in N` and are in lowest form, then find the value `(a + b)/(25)`

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The correct Answer is:
4
`6x + y = +9`
Equation of perpendicular line from `(-3, 1)`

`y - 1 = (1)/(6)(x + 3)`
`6y - 6 = x + 3`
`rArr x - 6y + 9 = 0 rArr 6x - 36y + 54 = 0`
`rArr 6x + y - 9 = 0`
`-37y + 63 = 0`
`y = (63)/(37) = (a)/(b)`
`a + b = 100`
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