Question

what is the function rule represented by the following table?x y0 31 -12 -5

Answer 1

We have the next table

x y

0 3

1 -1

2 -5​

First, we have the value of y in x=0 that is y=3, so that gives us the y-intercept that is 3, then we need to find the slope using two points of the table

(0 3)=(x1,y1)

(1 -1)=(x2,y2)

$m=\frac{-1-3}{1-0}=\frac{-4}{1}=-4$

the function rule will have the next form

y=mx+b,

where m is the slope and b the y-intercept,

if we substitute the values we obtain the function rule, that is

$y=-4x+3$