Question

Analytic Geometry: Family if Lines

Problem: Find an equation representing each family of lines described. Identify and Sketch three members of the family passing through the intersection of 4x-5y = 14 and 7x+3y = 1.

Answer 1

I think the family of lines must satisfy :
\[\large \rm (3x-5y-14) + t(7x+3y-1) = 0\]

Answer 2

you will get different lines passing through the intersecting point for different values of \(\rm t\)

Answer 3

@ganeshie8 t stands for??

Answer 4

\(\large \rm t\) is a parameter

Answer 5

it could be any real number

Answer 6

@ganeshie8 is it \[\left( 3x - 5y -14 \right) + t \left( 7x + 3y - 1 \right) = 0\] or \[\left( 4x - 5y -14 \right) + t \left( 7x + 3y -1 \right) = 0\] ??

Answer 7

Ahh sorry there was a typo, your second equation is correct

Answer 8

just cookup the equation using the given two lines