ShmoopTube

00:04

Solving Systems by Graphing a la Shmoop. The mayor of New Chunk City has banned all

00:13

sugary beverages larger than sixty-four ounces.

00:19

You've heard from a friend that Black's Market is selling sixty-four ounce sodas in the alleyway

00:24

behind the store.

00:27

Unfortunately, you don't know where Black's Market is, and all you have are a couple of

00:33

cryptic equations leading the way there.

00:36

Graph the equations, and they'll provide you with the coordinates to sugar overload.

00:40

Here's the scrap of paper your friend gave you.

00:45

We'll tackle the equations by changing them to slope-intercept form first...

00:50

Let's start with the top equation...

00:52

negative-three-x plus y equals six. You can do this one without sugar and caffeine

00:57

coursing through your veins.

00:59

Just add three-x to both sides. Doing that, we see that y equals three-x plus six.

01:05

The second one is slightly trickier. But if you can mix Coke and Pepsi until it tastes

01:09

like Dr. Pepper, this is nothing.

01:11

First, subtract x from both sides, giving us two-y equals negative x minus 2.

01:19

Then just divide all the terms by two.

01:21

We end up with y equals negative one-half x minus 1.

01:26

Now we just have to graph them.

01:29

We'll do the first equation in blue.

01:33

The y-intercept is 6, so we can plot a point at zero-six, which is six up the y-axis.

01:40

Because we know slope is rise over run, for every one we run or move to the right along

01:45

the x axis, we rise, or move three up the y-axis.

01:49

Reversing this, we move three spaces down the y-axis for every one we move left along

01:55

the x-axis.

01:57

The blue line will intersect the x-axis at negative-two, zero.

02:02

We'll do the second equation in red.

02:04

The y-intercept is negative 1, so we can plot a point at zero, negative-one on the y-axis.

02:11

For every one we run, or move right along the x-axis, we'll move one-half down.

02:17

Flipping that, we'll move 1/2 up for every one we move left along the x-axis.

02:21

This line, too, intersects the x-axis at negative-two, zero.

02:29

So that's where the Black's Market is.

02:32

At (-2, 0).

02:34

You may have to take the subway there, but we're pretty sure you'll be able to run back

02:37

home on a pure sugar rush.

Full Transcript