The straight line graph y=2x+k intersects the x-axis at pointA and y-axis at point B.Given that the length of AB is `sqrt(5)` units,find the values of k

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The line y=2x+k , meet x axis at A, Thus coordinate of A is (-k/2,0).

meet y axis at B, Thus coordinate of B is (0,k).

distance beetween A and B =sqrt(5)

But by distance formula

`AB=sqrt((x_1-x_2)^2+(y_1-y_2)^2)`

`sqrt(5)=sqrt((-k/2)^2+k^2)`

squaring both side ,we have

`5=k^2/4+k^2`

`5=k^2(1/4+1)`

`k^2=4`

`Thus`

`k=+-2`

Thus line is

`y=2x+-2`

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