Equation Formula?

Question

write an equation for f (x) from the table below

x -2 -1 0 1 2
f(x) -5 -2 1 4 7

Answer 1

__x |- 2__-1__0__1__2
f(x) |- 5__-2__1__4__7

f(x) = 3x + 1

Answer 2

okay, the first thing that we need to do i sto figure out if this equation is linear or not. to do this, we must find the differnces between one f(x) term and its preceding. if the difference is constant the equation is linear
-2-(-5)=-2+5=3
1-(-2)=1+2=3
already we know that the equation is linear, and so we must use the equation that is the standard form of a linear equation. the formula is y=mx+b
in this, m is the slope of the line, which can be found by using the equation m=(y2-y1)/(x2-x1). in this case, y is expressed as f(x). so the real equation for the slope is m=(f(x)2-f(x)1)/(x2-x1).
this means that we can use any 2 value pairs.
lets use the first two:
-2,-5
-10,-2
input these into the equation.
m=((-2)-(-5))/((-10)-(-2))
m=(-2+5)/(-10+2)
m=3/-8
or
m=-3/8
now that we know the slope, we can input this into the equation y=mx+b, or in this case f(x)=mx+b
f(x)=mx+b
f(x)=(-3/8)x+b
now we must solve for b, the y-intercepts. in other words, the value of y when x=0.
to do this we must use yet another value pair (we can use one of the ones we used b4).
lets use -2,-5
f(x)=(-3/8)x+b
-5(-2)=(-3/8)(-2)+b
-5(-2)=(3/8)(2)+b
-5(-2)=6/8+b
-5(-2)=3/4+b
b=-5-(3/4)
b=-5 3/4
or
b=-23/4
input this into the equation we had so far:
f(x)=(-3/8)x+b
f(x)=(-3/8)x+(-23/4)
f(x)=(-3/8)x-(23/4)
and thats ur answer
unless u want it in simpler form so u do not end up adding fractions:
f(x)=(-3/8)x-(46/8)
f(x)=(-3x-46)/8
f(x)=-(3x+46)/8
i no y i messed up bad because the 1 and the 0 i read as 10, but the real answer is 3x+1=f(x).

Answer 3

find slope
m = (y2-y1)/(x2-x1)
m = (-5-(-2))/(-2-(-1))
m = (-3)/(-1)
m = 3
use point slope form
y-y1 = m(x-x1)
y-y1 = 3(x-x1)
y-(-2) = 3(x-(-1))
y+2 = 3x+3
y = 3x+1
substitute f(x) for y
f(x) = 3x+1

Answer 4

x -2 -1 0 1 2
f(x) -5 -2 1 4 7
common difference in f(x) = 3
so this is a linear relation,
f(x) = 3x +c, now sub.any pair to get c,for instance,( 0 , 1 )
1 = 3(0) +c
c = 1
f(x) = 3x +1

Answer 5

graph the points:
(-2, -5) (1,-2) (0,1) (1,4) (2,7)

determine the equation of the curve or line.

you're done, and more importantly, you can do the next ones.

Answer 6

use slope formula first pick two points then (y2-y1)/(X2-X1)=m

then pick one point and use y-y1=m(x-x1)

then you should get the equation.

Answer 7

f(x) = 3x + 1