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x + by + c = 0 has an x-intercept of 4. x + 2by + c = 0 is parallel to x + by + c = 0,...
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Let's rearrange the equations of the lines as below.
`x+by+c = 0`
`by = -x-c`
`y = -1/bx-c/b`
This has a x intercept of 4. That means when y = 0, x=4.
`4+0+c = 0`
`c = -4`
`x+2by+c = 0`
`2by = -x -c`
`y = -1/(2b)x-c/(2b)`
The given equations are parallel. Therefore,
`-1/b = -1/(2b)`
`2b = b`
This can only happen only if `b = 0` .
Therefore, the both equations reduces
`x+c = 0`
`x-4 = 0`
Therefore the x-intercept of second equation is also 4.
Posted by thilina-g on June 1, 2012 at 4:59 PM (Answer #1)
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