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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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asicannot | Student, Kindergarten | eNoter

Posted June 1, 2012 at 4:45 PM via web

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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, what is the x intercept.

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thilina-g | College Teacher | (Level 1) Educator

Posted June 1, 2012 at 4:59 PM (Answer #1)

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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.

This gives,

`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`

`c =-4`

`x-4 = 0`

 

Therefore the x-intercept of second equation is also 4.

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