How to write an equation to represent a function from a table of values?

let start

this value represent a function that passes through the points in the xy axis

the standard function is :

y=mx +n

you can solve this equation in two ways :

1.pure substation

use two point from the given values to find m and n

e.g

(-4,14)

y=mx+n

14= -4m +n

(-3,11)

11 =-3m +n

now you can use either substation or replacement to find n and m

i.e

14= -4m +n

-

11 =-3m +n

_______________

14-11= -4m +3m +n -n

3 = - m

m=-3

now you can find n with the new function and any point

y=-3x +n

(-4,14)

14 =-3(-4) +n

14 =12 + n

n=2

the function is

y=-3x +2

you should always check your answer ,with another point in the x,y axis , and make sure that it gives a correct statement

e.g

(-1,5)

y=-3x +2

5=-3(-1) +2

5=5 true

the second way to go is

by calculating m

via the following equation

m = (y2 -y1) / (x2 -x1)

e.g

(–2,8)

(–1,5)

m= (8 -5)/ (-2 +1) =3/-1 =-3

now you can use

y=-3m +n , with another point to calculate n

um wow yeah I have trouble too im a sixth grader and I haven't answered like 5 algerbra problems