How to prove that x a + y b = 1 where a is the x-intercept and b is the y-intercept for all a , b ≠ 0

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How to prove that             x      a        +            y      b        =  1   where     a is the     x-intercept and     b is the     y-intercept for all     a  ,  b  ≠  0

Sariah Glover · Accepted Answer

If the x intercept is a then   (  a  ,  0  ) is on the line. If y-intercept is b then   (  0  ,  b  ) is on the line. Now you have two points of the line and can get its formula. The slope between thse points is   m  =            (      0      −      b      )              (      a      −      0      )        =            −      b        a  . So the equation of line is   y  =  m  x  +  b  =            −      b      x        a    +  b. Now rearrange as   y  +            b      x        a    =  b divide by   b to get       y    b    +      x    a    =  1.

Banguizb · Accepted Answer

Equation of the line is  A  x  +  B  y  +  C  =  0If   x-interception is   M  (  a  ,  0  ) and y-interception is   N  (  0  ,  b  ) then they need to satisfy line equation  A  a  +  C  =  0  ;    B  b  +  C  =  0from which you can find  A  =  −      C    a    ;    B  =  −      C    b  After substituting to line equation  −      C    a    x  −      C    b    y  =  −  Cor      x    a    +      y    b    =  1

How to prove that <mstyle displaystyle="true" scriptlevel="0"> x a </mf

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