find the rule of this function

Question

x: 0   2   4   6   8

y: 6   5   4   3   2

Answer 1

Hello, Kate

 

Verbally, the rule is whenever x increases by 2, y deceases by 1.

Mathematically, the function (equation, rule) will be y= .5x + 6.  This is how. 

 

What they gave you is a function table.  From this function table we can glean the values of x and y, or the input and out put.  So, the points are (0,6) (2,5) (4,4) (6,3) (8,2). Remember that Y=mx+b, where m= slope and b is the y-intercept.

 

The y-intercept is the value of y when x=0. Now if you look at the points, when x=0, y=6.  So, b must be equal to 6.

To find the slope, I will use the slope formula.  You can pick any two points.  I am going to pick:

 

1) (0,6)  which I will called (x1, Y1)

2) (2,5)  which I will called (x2, y2)

 

Now, you might recall that the formula for the slope is

[(y2-y1)]/ [(x2-x1)]=       Plugging the values for x1,x2, y1, and y2 from above

[(5-6)]/[(2-0)]=              Subtracting

(-1)/2 or -.5                    This is the slope, which is the m value in y=mx + b

 

So, since b=6 and m= -.5, the equation( rule) will be y= -.5x+6

I hope this helps you out, and thanks for posting the question.

D. Y. Taylor

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