Relations

The equation, y= 5x+2, is a relation. A relation is defined as a set of ordered pairs that abides to a specific rule.
So with the equation, y= 5x+ 2, the specific rule that applies to it is:

When, x = 3
y = 5(3) + 2
y = 15 + 2
y = 17

That is the ordered pair in this case is, x =3 , y = 17 i.e. (3, 17)

Note: y = 5x+ 2 , is the same as, x → 5x+ 2
Where, x → 5x+ 2 reads ‘x is mapped to 5x+ 2’.

Relations can be showed using arrow diagrams. The following arrow diagram shows the relation between, x and y values for the equation, y = 5x+ 2.

Note: The y values in the arrow diagram above, were obtained by substituting the respective x values in the equation, y =5x + 2, for x.