Question

Answer this multiple choice question please, and thank you.

Answer 1

Table 3

Explanation:

A linear relationship will have constant rate of change(slope) for all x values

Rate of change = Δf(x)/Δx

where Δf(x) = change in values of f(x)

and Δx = corresponding change in values of x

Only table 3 has this constant rate of change:

• Between x = -1 and x = 0,
  Δf(x) = -1 - (-3) = -1 + 3 = 2
  Δx = 0 - (-1) = 1
  Δf(x)/Δx = 2/1 = 2
  
• Between x = 1 and x = 3,
  Δf(x) = 5 - 1 = 4
  Δx = 3 - 1 =2
  Δf(x)/Δx = 4/2 = 2
  
  

This slope of 2 is the same if you take any two pairs of x, f(x) values in that table

Hence constant slope = linear relation