The function of the data is [tex]f(x)=-\frac{3}{2} x+\frac{3}{2}[/tex].
Solution:
Let y = f(x)
Take any two points on the table.
(-3, 6) and (3, -3)
So [tex]x_1=-3, y_1=6, x_2=3, y_2=-3[/tex]
Slope of the line:
[tex]$m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]$m=\frac{-3-6}{3-(-3)}[/tex]
[tex]$m=\frac{-9}{6}[/tex]
[tex]$m=-\frac{3}{2}[/tex]
Using point-slope formula:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]$y-6=-\frac{3}{2} (x-(-3))[/tex]
[tex]$y-6=-\frac{3}{2} (x+3)[/tex]
[tex]$y-6=-\frac{3}{2} x-\frac{9}{2}[/tex]
Add 6 from both sides, we get
[tex]$y=-\frac{3}{2} x+\frac{3}{2}[/tex]
[tex]$f(x)=-\frac{3}{2} x+\frac{3}{2}[/tex]
The function of the data is [tex]f(x)=-\frac{3}{2} x+\frac{3}{2}[/tex].
