What should be the value of b for the line 3x + by - 8 = 0 to be parallel to x - y = 0. What would be its x and y intercepts.

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The line x - y = 0 can be rewritten as y = x which has a slope of 1. Two parallel lines have the same slope.

3x + by - 8 = 0

=> by = 8 - 3x

=> `y = (-3/b)x + 8/b`

The slope of this line `-3/b = 1`

=> b = -3

Substituting b = -3 gives 3x - 3y = 8. This can be written as:

`x/(8/3) - y/(8/3) = 1`

The x and y intercepts of the line are `8/3 and -8/3` respectively.

**The required value of b = -3 and the x and y intercepts of the resulting line are `8/3` and `-8/3` respectively.**

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