Function Tables

[ataylor1209]

I am helping my nephew with his pre-algebra and we are stuck on this one function table the others were easy, but I can't seem to come up with a rule for this one:

In-----Out
0 2
1 1.5
2 1
3 0.5

I see the pattern that the input is increasing by 1 and the output is decreasing by 0.5, but I can't figure out a rule that will give me the desired output.

 

[Denis]

In-----Out
0 2
1 1.5
2 1
3 0.5

0, 2 - 0*.5
1, 2 - 1*.5
2, 2 - 2*.5
3, 2 - 3*.5

 

[lenguyen]

The rule will come up with the linear equation: y= mx + b which m is the slope and b is the y_ intercept.
Step1: Find the slope:
consider that the input is x and the output is y
Choose any pair of x and y (x, y)
You may choose (0,2) and (1,1.5) as (x1, y1) and (x2,y2)
slope m= (y2-y1)/(x2-x1)
m= (1.5-2)/ (1-0)
m= -0.5
Step 2: Find the y-intercept
_ Choose one of the 2 pairs that is using above
You may choose (0,2)
Plug in the point (0,2) and the slope m=-0.5 to the equation y= mx+b
So that you have 2= (-0.5)(0)+b
2= 0 + b
2= b
Step 3: plug in m= -0.5 and b= 2 to the equation y= mx+b
The equation will be y= -0.5x+2
It is the rule for your problem
Good Luck!