ShmoopTube

00:03

Here’s an unshmoopy question you’ll find on an exam somewhere in life.

00:07

The following set of coordinate points consists of the values of x and the corresponding values of y.

00:14

{(0, 5), (1, 3), (2, 1), (3, -1)}.

00:17

Which of the following represents the relationship between x and y?

00:21

And here are the options…

00:26

It’s plug’n’chug time.

00:27

One of the equations will satisfy ALL of the given coordinate points.

00:31

We just have to do some detective work and find which one it is.

00:34

Let's start with A… the given equation is y equals x plus 5.

00:39

Does that satisfy the coordinate (0, 5)?

00:42

Well, if we plug in 0 for x and 5 for y: 5 = 0 + 5.

00:47

So far so good. How about the second coordinate, (1, 3)?

00:51

Let’s try it out: 3 = 1 + 5.

00:56

Hmm, only in an Orwellian negative utopia does 1 plus 5 equal 3.

01:01

We can scrap A. Moving on to option B… y equals 2x plus 1.

01:06

Plug in the first coordinate: 5 = 2(0) + 1.

01:10

Nope, 5 does not equal 0 + 1. We can say goodbye to B.

01:14

Option C is y equals 2x minus 3. Let’s plug in (0,5).

01:19

Does 5 equal 2(0) – 3? No, 5 does not equal negative three.

01:26

Last chance, so let’s make it a good one… option D.

01:29

The equation is y equals negative 2x plus 5.

01:34

Plug in (0,5): 5 equals negative 2 times 0 plus 5. 5 does equal 0 plus 5.

01:43

Let’s try the second coordinate: (1,3). Is 3 equal to negative 2 times 1 plus 5?

01:49

Yup, 3 equals -2 plus 5. We’re on a roll!

01:56

Just to be sure, we’re going to plug the last two coordinates into the equation.

02:00

Is 1 equal to negative two times 2 plus 5? Yup, negative 4 plus 5 equals 1.

02:08

And the last one… is negative 1 equal to negative 2 times 3 plus 5?

02:14

Yeah, negative 1 equals negative 6 plus 5.

02:17

D satisfies all of the coordinates.

02:19

As in, “Detective Retirement Community.”

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