How do you this? write a equation from this function. idk

The input is the x value. The output is the y value. The question is asking for a function which will give you the output when the x value is plugged in. The input is increasing by 1 each time. The output is decreasing by 3 each time. -3÷1=-3. Therefore, x is going to be multiplied by -3. However, -3x does not equal the Y-value so one must determine if something is being added. -3×1=-3 =/= -1. However, (-3×1)+2=-1. -3x+2 is a possible function of Y. To check, one can plug in the rest of the X values to determine if the answer will be equal to the Y value given in the table.
Therefore: Y=-3x+2.

Slope
m = (y sub 2 - y sub 1)/(x sub 2 - x sub 1)
using points (1,-1) as pair one and (4, -10) as pair 2
m = (-10-(-1))/(4-1)
m = (-10+1)/(3)
m = (-9)/(3)
m = -3/1
m = -3
function
y - y sub 2 = slope( x - x sub 2)
y - (-10) = -3(x - 4)
y + 10 = -3x +12
-10. -10
y = -3x + 2
f(x) = -3x + 2