Home > Geometry calculators > Coordinate Geometry > Find the equation of a line passing through point of intersection of lines 4x+5y+7=0 and 3x-2y-12=0 and point A(3,1)

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Problem: line through intersection point of 4x+5y+7=0, 3x-2y-12=0 and (3,1) [ Calculator, Method and examples ]

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Your problem `->` line through intersection point of 4x+5y+7=0, 3x-2y-12=0 and (3,1)


The point of intersection of the lines can be obtainted by solving the given equations.
`4x+5y+7=0`

`:.4x+5y=-7`

and `3x-2y-12=0`

`:.3x-2y=12`

`4x+5y=-7 ->(1)`

`3x-2y=12 ->(2)`

equation`(1) xx 2 =>8x+10y=-14`

equation`(2) xx 5 =>15x-10y=60`

Adding `=>23x=46`

`=>x=46/23`

`=>x=2`

Putting `x=2` in equation `(2)`, we have

`3(2)-2y=12`

`=>-2y=12-6`

`=>-2y=6`

`=>y=-3`

`:. x=2" and "y=-3`

`:. (2,-3)` is the intersection point of the given two lines.


Here `A(3,1), (2,-3)` are the given points

`:. x_1=3, y_1=1, x_2=2, y_2=-3`

The equation of a line AB is
`(y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1)`

`:. (y-1)/(-3-1)=(x-3)/(2-3)`

`:. (y-1)/(-4)=(x-3)/(-1)`

`:. -(y-1)=-4(x-3)`

`:. -y +1=-4x +12`

`:. 4x-y-11=0`










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