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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