find the Function rule
x: -2,-1,0,1,2
y: -1,1,3,5,7
Average rate of change of linear function is slope.
m = [ f(b) - f(a) ] / ( b - a )
For a linear function, the slope is constant.
In this case:
x1 = - 2 , y1 = - 1
x2 = - 1 , y2 = 1
x3 = 0 , y3 = 3
x4 = 1 , y4 = 5
x5 = 2 , y5 = 7
( y2 - y1 ) / ( x2 - x1 ) = [ 1 - ( - 1 ) ] / [ ( - 1) - ( - 2 ) ] = ( 1 + 1 ) / ( - 1 + 2 ) = 2 / 1 = 2
( y3 - y2 ) / ( x3 - x2 ) = ( 3 - 1 ) / [ 0 - ( - 1 ) ] = 2 / ( 0 + 1 ) = 2 / 1 = 2
( y4 - y3 ) / ( x4 - x3 ) = ( 5 - 3 ) / ( 1 - 0 ) ] = 2 / 1 = 2
( y5 - y4 ) / ( x5 - x4 ) = ( 7 - 5 ) / ( 2 - 1 ) ] = 2 / 1 = 2
So the slope:
m = 2
Put this value for any pair of coordinates in poit-slope fotmula for example for x4 = 1 , y4 = 5
y = m x + b
y = 2 x + b
5 = 2 ∙ 1 + b
5 = 2 + b
5 - 2 = b
3 = b
b = 3
y = 2 x + 3