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)

Solve any problem
(step by step solutions)
Input table (Matrix, Statistics)
Mode :
Problem: line through intersection point of 4x+5y+7=0, 3x-2y-12=0 and (3,1) [ Calculator, Method and examples ]

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.


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


`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`



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





`:. 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-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`

Solution provided by AtoZmath.com
Any wrong solution, solution improvement, feedback then Submit Here
Want to know about AtoZmath.com and me

Copyright © 2019. All rights reserved. Terms, Privacy

We use cookies to improve your experience on our site and to show you relevant advertising. By browsing this website, you agree to our use of cookies. Learn more