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## 8th grade (Eureka Math/EngageNY)

### Course: 8th grade (Eureka Math/EngageNY) > Unit 4

Lesson 2: Topic B: Linear equations in two variables and their graphs- Rates & proportional relationships example
- Rates & proportional relationships: gas mileage
- Rates & proportional relationships
- Graphing proportional relationships: unit rate
- Graphing proportional relationships from a table
- Graphing proportional relationships from an equation
- Graphing proportional relationships
- Points on the coordinate plane examples
- Testing solutions to linear equations
- Solutions to 2-variable equations
- Graphing a linear equation: 5x+2y=20
- Complete solutions to 2-variable equations

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# Points on the coordinate plane examples

The coordinate plane is a two-dimension surface formed by two number lines. One number line is horizontal and is called the x-axis. The other number line is vertical number line and is called the y-axis. The two axes meet at a point called the origin. We can use the coordinate plane to graph points, lines, and more. Created by Sal Khan and CK-12 Foundation.

## Want to join the conversation?

- why do you have to start with the y axis than the x axis first

(281 votes)- Always start with X then Y I like to think of it alphabetically.(43 votes)

- Is there a reason that we use the "X" axis first?(19 votes)
- Yes. When plotting points, we start with the number we start with (the independent variable, x), then we use the number we end with (the dependent variable, y). The independent variable is always first, so we use the x axis first.(22 votes)

- please get me 10 upvotes(21 votes)
- at about4:00how come Sal only puts four dash marks on his coordinate plane instead of more when he could have easily fit more than that?(8 votes)
- just because he can't fit every single solitary number into one small screen(3 votes)

- McDonalds or chic-fil-a(8 votes)
- Chic-fil-a, their strawberry milkshakes are to die for(2 votes)

- Was Descartes the one who taught the convention that the x comes first in (x,y)?

Please help because I really need help(3 votes)- Rene Descartes is credited for the introduction of Cartesian geometry, so it should be safe to say he is the one who fostered the convention that x comes before y. Also it makes sense since x comes before y in the alphabet.(9 votes)

- why are the quadrants counter clockwise?(5 votes)
- Some of these things are simply named by convention, but I also think it may have something to do with the way that we "sweep out" angle in trigonometry; clockwise from the positive x-axis. I'm not really sure if that's why, but it seems applicable.(4 votes)

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¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶¶(6 votes) - why cant the x axis go up and down and why cant the y axis go side to side(3 votes)
- The way that axes work is just our convention. If you want a q-axis and an m-axis, then be my guest. X is usually used to refer to a horizontal direction/motion, and Y refers to vertical. This is just the way some person thought of it, and this is the way we've been doing it for the past hundreds of years.(6 votes)

- why Are the y axis and the x axis always have to be apart(3 votes)

## Video transcript

What we're going to do in this
video is, through a bunch of examples, familiarize
ourselves with the x,y-coordinate plane. And first we're going to just
look at some points that are already plotted and figure
out their coordinates. Then we're going to look at some
coordinates and figure out where those points are. Then we'll do one
more problem. So let's figure out
what are the coordinates of these points? So you have this point
right here, A. So its x-coordinate, you
can see it right there. You just drop down. Where does it intersect
the x-axis? x is equal to 5. So it's the point 5 comma and
y is going to be equal to 6. 5 comma 6. Now this point B here, what's
the x-coordinate? It is 5 to the left. 5 to the left of the x-axis. This is negative 5. Its x-coordinate
is negative 5. y-coordinate is, if you just
go straight to the right, you're going to hit
y is equal to 5. y is equal 5. Let me switch colors. C. I think you're getting
the hang of this. Let's do the y-coordinate first.
The y-coordinate is 3. You see that right there. And then the x-coordinate
is negative 2. Negative 2. You always put the x-coordinate
first. That's just the convention we use. D, x-coordinate negative 2. You see that right there. y-coordinate negative
2, as well. Let me get another color. E, let's do the y-coordinate. We'll figure it out first,
but you always have to write it second. It's negative 4. You see that right there,
the y-coordinate. The x-coordinate is 3. And then finally, F. The x-coordinate is 2. And the y-coordinate
is negative 6. Hopefully that gives you a sense
of at least figuring out the coordinates. Now let's go the other way. Let's start with coordinates
and figure out where those points are. So you have this first one. I'll do it lowercase case a in
parentheses to differentiate it from this uppercase A. So it's at 4 comma 2.
x is equal to 4. y is equal to 2. So that's that point
right there. Let's do the next one. Let me do it in a color that
you'll be able to read. b. x is equal to negative 3. y is equal to 5.5. So you go all the
way up to 5.5. y is equal to 5.5. So that is the point lowercase
b with parentheses around it. Then c, 4 negative 4.
x is equal to 4. y is equal to negative 4. Right over there. And then one last one. I'll do it in orange. d, x is negative 2,
y is negative 3. Right there. That's the d with parentheses. And you could have gone
the other way. You could have said, hey, y
is equal to negative 3. x is equal to negative 2. So you could go to the
left and down. Or you could go down
and to the left. And you're still going to
get to the same point. So hopefully that gives you a
good sense of how to figure out coordinates. Or if you're given coordinates,
how to figure out where to plot something on
the x,y-coordinate plane. Now let's do a slightly
more involved problem. So it says the following 3
points are 3 vertices of square A, B, C, D. Plot them on a graph. Then determine what the
coordinates of the fourth point, D, would be. All right, let's plot
these on a graph, as they tell us to do. All right. That'll be my y-axis. That's my y-axis. The vertical axis. That'll be my x-axis. And let me put some--
let me mark it. So that's x equals 1, 2, 3, 4. This is x is equal to negative
1, negative 2, negative 3, negative 4. That's y is equal
to 1, 2, 3, 4. This is y is equal to negative
1, negative 2, negative 3, negative 4. I could write that
this y equals 4. This y equals negative
4. x is equal to 4. x is equal to negative 4. And let's see. Let's plot these points. So first, we have the point
A is equal to negative 4, negative 4. So we go x is negative 4. And then y is negative 4. So we drop down 4 right there. And that is our point A. Negative 4, negative 4. And just to familiarize yourself
with a labeling scheme that you may or may not
have seen before, is that people label these sections
of the coordinate plane. They call this the
first quadrant. They call this the
second quadrant. They call this the
third quadrant. And they call this the
fourth quadrant. And these are just the Roman
numerals for I, II, III, and IV, So this point is in
the third quadrant. When we looked up at this stuff
over here, these points are in the fourth quadrant. These are in the third,
second, first. Just an interesting thing to know. Sometimes someone might
ask you, what quadrant is that point in? And you just say, OK, I see. If they're both negative,
they're going to be in the third quadrant. If just the y is negative, but
the x is positive, you're going to be in the fourth. If they're both positive, you're
in the first. If y is positive, but x is negative,
you're in the second. And we'll talk a little
bit about that as we plot these points. So point B, x is positive. It's 1, 2, 3. And y is negative 4. So we drop down here into
the fourth quadrant. That is the point B. It's 3, negative 4. So we can already see the bottom
of our rectangle that they're talking about,
right there. And notice, both of these
have the exact same y. They're both at the same
level below the x-axis. And then what's the
next point? Point C is 3 comma 3. So 3 comma 3. It's in the first quadrant. Both of its coordinates
are positive. 3 comma 3. Both x and y are positive. And notice, it's on the
same vertical as B. It has the same x value. They both have an
x value of 3. So it's right above it. Right above it. Now we have to figure out
the last point here. Well, the point is going to
have to be on the same vertical as this point. It's going to have to be on
the same vertical as this point, which means it's going
to have the same x value as this point. So its x value is going
to be negative 4. And then it's going to have to
be on the same horizontal as this point. It's going to have
to be on the same horizontal as that point. So it's going to have to have
the same y value at the same height above the x-axis. So it's going to have to be 3. So that is our point D. Notice it's at negative
4, right above A. And it's at y is equal to 3. Right to the left of point C. And we are done.