Question

What is the function rule when the input is 0,1.2.3 and the output is 5,4,3,2?

Answer 1

x: 0 1 2 3
y: 5 4 3 2
to get the function, we choose two points. let's just choose the first two points,, that is, point1 (0,5) and point2 (1,4)
now, we get first the slope. the slope is given by the equation,
slope = m = (y2 - y1)/(x2 - x1)
where
y1 = y-coordinate of point1
x1 = x-coordinate of point1
y2 = y-coordinate of point2
x2 = x-coordinate of point2

for point1=(0,5) and point2=(1,4)
y1 = 5 , x1 = 0 , y2 = 4 and x2 = 1
substituting,
m = (y2 - y1)/(x2 - x1) = (4-5)/(1-0) = -1/1 = -1
then we substitute it in the slope-intercept form equation:
y - y1 = m(x - x1)
substituting with y1 = 5, x1 = 0 and m = -1,
y - 5 = -1(x - 0)
y - 5 = -x
x + y - 5 = 0
x + y = 5

hope this helps~ :)