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#1 2021-12-02 12:39:55

Hannibal lecter
Registered: 2016-02-11
Posts: 330

intersect of two lines

how to check if the lines is has intersect point or not without graph just from numbers and quations!
for example for these lines
c1= 40 + 0.15m 
c2 = 50 + 0.10m
I know I do c1=c2 and intersect point is 200

but what if the lines are not intersected what result I'll get?

Wisdom is a tree which grows in the heart and fruits on the tongue


#2 2021-12-02 22:36:02

Registered: 2010-06-20
Posts: 9,358

Re: intersect of two lines

hi Hannibal lecter

In a previous post you said you don't want to hear about slope and  linear equations.  It's very hard to answer your questions without.  There are excellent teaching pages on this on the main MathsIsFun website.  I recommend you start with this page:

If two lines are parallel they will never cross.  If not parallel, they will cross.

The slope of a line is determined by the number in front of the x (or m in your example); so in your post the relevant numbers are 0.15 and 0.10.  As these are different, the lines are not parallel, so they will cross.

Let's see what happens with parallel lines.

c1= 40 + 0.15m
c2 = 50 + 0.15m

They will cross when they have the same y coordinate so when c1 = c2

Let's put those equal and see what happens.

40 + 0.15m = 50 + 0.15m

Cancelling the 0.15m terms we are left with 40 = 50 ?????

That is clearly not true, so the lines cross when something impossible happens.  In other words never.

If you try to find when a line crosses itself:

c1= 40 + 0.15m
c2 = 40 + 0.15m

Proceeding as before we have

40 + 0.15 m = 40 + 0.15m  => 40 = 40.

This always happens whatever c and m are. So the line crosses itself everywhere.


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile


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