Question

HOW can you decide whether a relationship is linear by studying the pattern in a data table?

Answer 1

For a relationship to be linear, there must be a constant rate of change. To check this, you need to calculate the equation of the line.
A linear line will always have an equation in the following pattern:
y = mx + c where m is the slope and c is a constant.
This equation must be of first degree (highest power is x^1) to be linear.

Note:
the slope can be calculated using two points (x1,y1) and (x2,y2) as follows:
m = (y2 / y1) / (x2 - x2)
You can then use points from the table and substitute in the equation to calculate the value of c.