find function of?

Question

x y
1 6
2 1
3 -4
4 -9
5 -14
6 -19


x y
1 6.5
2 7
3 7.5
4 8
5 8.5
6 9

Answer 1

1.) first find the slope of the points (y1-y2)/(x1-x2)
in this case its (6-1)/(1-2)=5/-1= -5
this means their is a -5x in the f(x)

then find what the y-intercept(b) is you do this by subsituting a random x an in the equation y+-5x+b
if you use 3, it would be -5(3)+b=-4 answer is 11

final equation is y=-5x+11

2.)Do the same thing, you get the slope is .5 and the intercept is 6, so the equation is y=.5x+6

Answer 2

A good way to start looking at these is to check out the differences between terms. In this case

6 - 1 = 5
1 - -4 = 5
-4 - -9 = 5
...
so it is of the form a - 5x. Make it work for the first one: if the first term is the 0th term then a-5*0 = 6 so a = 6. If you consider the first term term 1 then a - 5 = 6 so a is 11.

Try the same technique on the second:

6.5 - 7 = -.5
7 - 7.5 = -.5
7.5 - 8 = -.5
...
Success!

So the formula is a - .5. Plug in the first (I will call it the 0th), so the formula is 6.5 - .5x

Answer 3

y=11-5x
y=6+(1/2)x