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8. Find the equation of a line passing through point of intersection of two lines and slope or a point example
( Enter your problem )
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- Find the equation of a line passing through the point of intersection of lines 3x+4y=7 and x-y+2=0 and having slope 5
- Find the equation of a line passing through the point of intersection of lines 4x+5y+7=0 and 3x-2y-12=0 and point A(3,1)
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2. Find the equation of a line passing through the point of intersection of lines 4x+5y+7=0 and 3x-2y-12=0 and point A(3,1)
1. Find the equation of a line passing through the point of intersection of lines `x+y+1=0` and `3x+y-5=0` and point `A(1,-3)`
Solution:
The point of intersection of the lines can be obtainted by solving the given equations
`x+y+1=0`
`:.x+y=-1`
and `3x+y-5=0`
`:.3x+y=5`
`x+y=-1 ->(1)`
`3x+y=5 ->(2)`
Substracting `=>-2x=-6`
`=>2x=6`
`=>x=6/2`
`=>x=3`
Putting `x=3` in equation `(1)`, we have
`3+y=-1`
`=>y=-1-3`
`=>y=-4`
`:.x=3" and "y=-4`
`:. (3,-4)` is the intersection point of the given two lines.
The given points are `A(1,-3),(3,-4)`
`:. x_1=1,y_1=-3,x_2=3,y_2=-4`
Using two-points formula, The equation of a line A is
`(y-y_1)/(y_2-y_1)=(x-x_1)/(x_2-x_1)`
`:. (y+3)/(-4+3)=(x-1)/(3-1)`
`:. (y+3)/(-1)=(x-1)/(2)`
`:. 2(y+3)=-1(x-1)`
`:. 2y +6=-x +1`
`:. x+2y+5=0`
Hence, The equation of line is `x+2y+5=0`
2. Find the equation of a line passing through the point of intersection of lines `4x+5y+7=0` and `3x-2y-12=0` and point `A(3,1)`
Solution:
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.
The given points are `A(3,1),(2,-3)`
`:. x_1=3,y_1=1,x_2=2,y_2=-3`
Using two-points formula, The equation of a line A 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)`
`:. -1(y-1)=-4(x-3)`
`:. -y +1=-4x +12`
`:. 4x-y-11=0`
Hence, The equation of line is `4x-y-11=0`
This material is intended as a summary. Use your textbook for detail explanation.
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