Parametric Equatuon. Equation Of The Line

[David1717]

How can I transform parametrical equation into form of y=kx+b?
Suppose I have x=2-t and y=3+2t, where t is proportionality factor.

[jim360]

Short answer: Eliminate t.

Long answer: If x is 2-t then rearrange the equation to get t= 2-x. Then substitute this value of t into the equation for y, to get y = 3+2t = 3+2(2-x)= 3+4-2x = 7-2x = -2x+7.

So the equation of the line is y = -2x+7 as required.

[factor-fiction]

t=2-x
Substitute it into y=3+2t

[factor-fiction]

He was asking me, jim.

[jim360]

Well you should have been quicker then.

[wolf63]

I very nearly calculated it - but you two were so much quicker. I only took me 15 years to obtain my o'level maths.

[factor-fiction]

That's good, wolf- it took me 16 years

[jim360]

I never even got my O Level!

[wolf63]

And you teach maths? Why does that worry me a bit? What did you do before you were a teacher?

[wolf63]

jim - you are but a baby. Did they still have o'levels when you were at school?

[Prudie]

LOL like the humour

[factor-fiction]

We weren't allowed to take it until year 11 (5th form), wolf. But now I think about it, I took it a a couple of weeks before my 16th birthday and was pleased with my grade A. I was only 14 when I sat my English Language 'O' level.
That was in the days when it was rare to sit more than 8 'O' levels- many students now seem to sit 12 or more

[jim360]

Most students sit 12 GCSEs, which are easier than O Levels.

[factor-fiction]

Controversial, jim. I feel that the higher GCSE papers are similar to the old 'O' level papers in terms of difficulty whereas the Foundation papers (which cover grades G-C) are more like the old CSE papers, with a grade C being equivalent to the old CSE grade 1.
In Maths, though, it's true that some stuff we used to do at 'O' level (e.g.calculus including volumes of revolution) aren't covered until the first year of A level.
Also, the questions are less wordy now and there is always a helpful picture to make things easier for candidates

[jim360]

Well, perhaps I speak only for Maths, which is noticeably easier. Other subjects I've not had a chance to look at in such detail.

[vascop]

A more elegant way of doing this is to multiply equation 1 by 2 and add the equations together to eliminate t:
2x=4-2t
y=3+2t
Add to get:
y+2x=7

[SubjectTeachers]

What you can do is, you can find out the value of t from any of the given two equations, Let us take the value of t from equation 1: x = 2-t
So, t = 2 - x
Now, putting this value into the second equation, we get,
y = 3 + 2(2-x)
y = 3 + 4 - 2x
y = 7 - 2x
y = -2x + 7
Which is in the form of y = kx + b.