Question

is there a faster way on how to solve for the mathematical sentence of certain relations? ex.:{(-1,1),(-2,2),(-3,3)} and if there is,how?

Answer 1

What do you mean by "solve for the mathematical sentence of certain relations" ?

Answer 2

like,for example {(0,3),(1,5),(2,11),(3,21),(4,35),...} how are these ordered pairs related? (in a mathematical sentence)

Answer 3

By "a mathematical sentence" I presume you mean a sentence in an essay of some sort? Unclear.

Answer 4

nah,kinda like y=x^2-1..its long term for an equation

Answer 5

we can try to look at the first one to see if we can see a simple relation to it; when x=0; y=3

y = mx +3 is a good start; now try to fit the second point (1,5) in there to solve for m like this:

5 = m(1) + 3

5-3 = m = 2; so maybe this works?

y = 2x + 3; now of the point (2,11) fits, we know its a line equation :)

11 ?= 2(2) + 3
11 ?= 4 + 3
11 ?= 7 ....... it aint a line :)

Answer 6

there is no "fast" way to it; the more points yo have to work with, the more fine tuning you can do; but the messier and longer it gets

Answer 7

the original can be easily determined to be: y = -x tho

Answer 8

2 points can be determined by a line:

(X1)a + (Y1) = 0
(X2)a + (Y2) = 0 and solve for a,b and c

3 points can be solved for a quadratic:

(X1)^2a +(X1)b + (Y1) = 0
(X2)^2a +(X2)b + (Y2) = 0
(X3)^2a +(X3)b + (Y3) = 0 ; and it gets messier from there :)

Answer 9

i spose - the y parts is a better construct tho :)

Answer 10

that "solve for a b and c part was part of another thought in my head .. i really should learn to think of one thing at a time :)

Answer 11

oh,no wonder..just analyze on the given..like,on how the value of y became connected w/ value of x..

Answer 12

y is just denoted conventionally as the output for any given set of variable and constant inputs. The mathmatical model is an ideal which can be adjusted and fine tuned to predict the outcome of real world events.

x, by convention, is a cause; while y is what happens as a result.

When a ball is resting on the ground its position is at a relative height of 0 to the ground.

y = 0

When I kick a ball such that its initial velocity is 24 ft per second, it continues to travel in a straight path:

y = 24x + 0

....unless acted upon by an outside force; such as gravity.

y = -16t^2 +24t +0 is then a good approximation of the height of the ball for any given amount of time(x) ...