the ordered pairs below represent a relation between x and y.
(-3,0), (-2,4), (-1,8), (0,12), (1,16), (2,20)

could this set of ordered pairs have been generated by a linear function?

A. No, because the distance between consecutive x-value is different than the distance between consecutive x-values.
B. Yes, because the relative difference between y-values and x-values is the same no matter which pairs of (x, y) values you use to calculate it.
C. No, because the y-values decrease and then increase
D. Yes, because the distance between consecutive x-values is constant.

Yes, this set of ordered pairs have been generated by a linear function because the relative difference between y-values and x-values is the same no matter which pairs of (x, y) values you use to calculate it.

The correct option is (B)

What is graph?

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given are ordered pairs are: (-3,0) (-2,4)(-1,8)(0,12)(1,16)(2,20).

It can be seen that the there only unit increase in x coordinates and units increase in consecutive y- coordinates.

Now, if we set up the equation of line as:

Here, m =4 and b = 12

So the relationship is linear and represented by the equation

y=4x+12

Hence, the relative difference between y-values and x-values is the same no matter which pairs of (x, y) values you use to calculate it.

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