input (x) 0 2 4 8

Question

input (x) 0 2 4 8

output f (x) 20 18 16 12

 

What is the rule for this table

Answer 1

Can you see that these are (x,y) ordered pairs? 

(0,20)

(2,18)

(4,16)

(8, 12)

 

You could figure the slope between any two of these points. 

Slope = rise/run = Δy/Δx = y2 - y1    

                                           x2 - x1 

e.g.) 18 - 12 = 6 = -1

           2 - 8    -6

 

slope = -1

 

We know the y intercept because the point (0,20) is given. 

So I can write the equation that includes all these points using

y intercept form y = mx + b:  y = -x +20

 

The rule is "take the opposite (or the negative) of your input value and then add 20".

Answer 2

If you graph the points you will see they define a straight line. So essentially, the equation of that line will be the rule for the table. First find the slope of the line by selecting two points. I will select (0,20) and (2,18). The rise is -2 and the run is 2. The slope is equal to the rise/run which is equal to -2/2 which equals -1. Therefore the slope is -1. The y-intercept is given as one of the points. Specifically, the point (0,20) is on the y-axis and this is the y-intercept. Now put this information into the slope-intercept form of the linear equation. The slope intercept form is f(x)=mx+b where m is the slope and b is equal to the y-intercept. So the equation of the line is f(x)=-1x+20 and this is the rule for the table.