Answer:
The required function is [tex]y=\frac{-1}{2}x+2[/tex]
Step-by-step explanation:
Given : Function table,
x 2 4 6
y 1 0 –1
To find : Explain how to write a function rule from the table and then write a function rule?
Solution :
To determine the function is linear, quadratic or exponential we find the difference of y-values.
y from 1 to 0 is 1 and from 0 to -1 is 1.
So, the difference is same the function is linear.
The general point slope form of linear equation is [tex]y-y_1=m(x-x_1)[/tex]
m is the slope given as [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{0-1}{4-2}[/tex]
[tex]m=\frac{-1}{2}[/tex]
Substitute m and one point let (2,1) in general form.
[tex]y-1=\frac{-1}{2}(x-2)[/tex]
[tex]y-1=\frac{-1}{2}x+1[/tex]
[tex]y=\frac{-1}{2}x+1+1[/tex]
[tex]y=\frac{-1}{2}x+2[/tex]
Therefore, The required function is [tex]y=\frac{-1}{2}x+2[/tex]
