### Video Transcript

Given that π
is a relation from π₯
to π¦, where π exists in π₯ and π exists in π¦, which of the following equations
correctly expresses relation π
? Is it (A) π equals π plus one,
(B) π equals two π plus two, (C) π equals two π minus two, (D) π is equal to
two π plus two, or (E) π is equal to two π minus two?

Any relation π
contains a set of
ordered pairs of the form π₯, π¦. In the diagram shown, we have three
ordered pairs: negative one, zero; four, 10; and five, 12. We can therefore say that the
relation π
is the set of these three ordered pairs. We are asked to find the correct
equation that matches any value in π₯ π to a value in π¦ π. The easiest way to do this is to
substitute our values into each of the equations. Letβs begin with the ordered pair
negative one, zero.

We will let π equal negative one
and π equal zero. Zero is equal to negative one plus
one. This means that equation (A) does
work for the first ordered pair. Likewise, two multiplied by
negative one plus two is also equal to zero. This means that equation (B) also
works for the first ordered pair. In option (C), two multiplied by
negative one minus two is equal to negative four and not zero. This means that equation (C) is not
the correct answer. This is also true of options (D)
and (E) as negative one is not equal to two multiplied by zero plus two or two
multiplied by zero minus two. We can therefore rule out both of
these options.

We will now consider the second
ordered pair four, 10 for equation (A) and equation (B). This time, π is equal to four and
π is equal to 10. 10 is not equal to four plus
one. This means that equation (A) is
also incorrect. 10 is equal to two multiplied by
four plus two. This means that equation (B) holds
for the first and second ordered pairs. We can now move on to the third
ordered pair five, 12. Two multiplied by five plus two is
equal to 12. As equation (B) holds for all three
ordered pairs, this is the correct answer. The equation that correctly
expresses relation π
is π is equal to two π plus two.