Rule of correspondance for relations

I do know how to do it (mostly) but I am having trouble with a few. I guess the question is can I use negative numbers to solve them?

{(x,y): (1,2),(2,5), (3,8), , ,}

Question

Rule of correspondance for relations

I do know how to do it (mostly) but I am having trouble with a few. I guess the question is can I use negative numbers to solve them?

{(x,y): (1,2),(2,5), (3,8), , ,}

mathstudent55 · Answer

Can you tell if the relation is linear?

anonymous · Answer

You mean going in a straight line on a graph?

mathstudent55 · Answer

Yes. Can you tell if its graph is a straight line?

anonymous · Answer

my graph looks awful but yes it seems to be straight or linear.

mathstudent55 · Answer

Ok.
I'll tell you how you can tell if it is a line without graphing.
A linear relation has the following.
For an equal difference in x, there must equal difference in y.

mathstudent55 · Answer

I'll explain how that is used.

mathstudent55 · Answer

You have only 3 points given.
(1, 2), (2, 5), (3, 8)

mathstudent55 · Answer

Look at the first two points:
(1, 2) and (2, 5)
The difference in x-coordinates is 2 - 1 = 1
The difference in y-coordinates is 5 - 2 = 3
Ok so far?

anonymous · Answer

Well I also noticed the pattern it had. one right, three up. if that's what you mean.

mathstudent55 · Answer

Exactly. That shows the same slope between points which means a line.
Great observation.

anonymous · Answer

:D

mathstudent55 · Answer

The difference in x was 1 and the difference in y was 3.
Now let's look at the last two points.
(2, 5), (3, 8)
The difference is x is 3 - 2 = 1
The difference in y is 8 - 5 = 3
Again we have a difference in x of 1 and a difference in y of 3.

Since for the same difference in x (1), we get teh same difference in y(3), we are dealing with a straight line.

mathstudent55 · Answer

Now that we know we have a straight line, we can find the equation of the line.

mathstudent55 · Answer

Do you know how to find the equation of a line given two points?

anonymous · Answer

No

anonymous · Answer

Not really

mathstudent55 · Answer

Ok, no problem. I'll explain it to you.
There are several methods, but here is one of them.

mathstudent55 · Answer

The two-point equation of a line

A line that passes through points $(x_1, y_1)$ and $(x_2, y_2)$ has equation

$y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1)$

mathstudent55 · Answer

You can use any two points of your three given points.
Let's use the first two points (1, 2) and (2, 5)

anonymous · Answer

sorry my tracad is messing around. but the answer appears to be 3 over 1?

mathstudent55 · Answer

$y - y_1 = \dfrac{y_2 - y_1}{x_2 - x_1}(x - x_1)$

$y - 2 = \dfrac{5 - 2}{2 - 1}(x - 1)$

$y - 2 = \dfrac{3}{1}(x - 1)$

$y - 2 = 3(x - 1)$

$y - 2 = 3x - 3)$

$y = 3x - 1$

The equation gives you the rule of the relation.
Take the x value, multiply by 3, and subtract 1.
Try it with your 3 points, and you'll see that it works.

anonymous · Answer

Ok I see what you have there. If I try one with a different equation can you check to see I'm doing it right? Also can this only be done with linear equations?

anonymous · Answer

@mathstudent55 
(2,3) (4,4) (6,5)

y=x-1? or did I miss something?

anonymous · Answer

Actually that can't be right...

mathstudent55 · Answer

$y = \dfrac{1}{2}x + 2$

mathstudent55 · Answer

Sorry, but gtg.

anonymous · Answer

ok thanks though!

mathstudent55 · Answer

yw