Home > Geometry calculators > Coordinate Geometry > Find the equation of a line passing through point of intersection of lines 2x+3y+4=0 and 3x+6y-8=0 and having slope = 2

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Find line through intersection point of 2x+3y+4=0, 3x+6y-8=0 and slope=2

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Your problem `->` line through intersection point of 2x+3y+4=0, 3x+6y-8=0 and slope=2


The point of intersection of the lines can be obtainted by solving the given equations.
`2x+3y+4=0`

`:.2x+3y=-4`

and `3x+6y-8=0`

`:.3x+6y=8`

`2x+3y=-4 ->(1)`

`3x+6y=8 ->(2)`

equation`(1) xx 3 =>6x+9y=-12`

equation`(2) xx 2 =>6x+12y=16`

Substracting `=>-3y=-28`

`=>3y=28`

`=>y=28/3`

Putting `y=28/3 ` in equation `(1)`, we have

`2x+3(28/3)=-4`

`=>2x=-4-28`

`=>2x=-32`

`=>x=-16`

`:. x=-16" and "y=28/3`

`:. (-16,9.33)` is the intersection point of the given two lines.


The equation of a line with slope m and passing through `(x_1,y_1)` is `y-y_1=m(x-x_1)`

Putting `(-16,9.33)` for `(x_1,y_1)` and `m=2,` we get

`:. y-9.33=2(x+16)`

`:. (y-9.33)=2(x+16)`

`:. y -9.33=2x +32`

`:. 2x-y+41.33=0`








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