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The Coordinate Plane

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The Coordinate Plane

Adapted from: www.klvx.org/ed_med_services/teacherline

Modified by: Marie Purvis

Imagine the top surface of your desk stretching in every direction.

If it continued to spread , it would go right through your neighbor . . .

. . . and then through the classroom walls . . .

. . . and through the school and the hills and the mountains and out into space until it went on forever in every direction.

Then you would have a plane.

In math, a plane is a flat surface that goes on forever in every direction.

In Algebra, it is often called the coordinate plane.

The coordinate plane is divided by two number lines. One is horizontal, like the number line you already know.

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The other is vertical, with up being the positive direction and down being the negative direction.

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The coordinate plane is filled with points . . .

. . . infinitely many points.

And somewhere among all those points is the point we call the origin.

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The origin is the point where the two number lines meet.

The two number lines have special names.

The horizontal number line is called the x-axis.

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The vertical number line is called the y-axis.

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The plural of axis is axes. We often talk about the coordinate axes.

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The two number lines divide the plane into four regions.

Quadrants are labeled with Roman Numerals.

We call the regions quadrants.

In Quadrant II, x-values are negative, while y-values are positive.

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In Quadrant I, all numbers are positive.

In Quadrant IV, x-values are positive and y-values are negative.

In Quadrant III, x- and y-values are both negative.

To study a point, we need to know where to find it. So we give it coordinates.

Coordinates are like an address. They tell you how you can get to a point if you start at the origin.

Coordinates are always written in parentheses, with the x-value first.

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Coordinates written in parentheses are called an ordered pair.

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Consider the point which has coordinates, (4, -2)

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The first number tells you how far to move to the side.

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So the 4 in (4, -2) says we need to move 4 units to the right.

Remember to start at the origin.

The second number tells you how far to move up or down.

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The –2 in (4, -2) tells you to move down two units.

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To get to the origin from the origin, we don’t move at all.

So the origin is designated by the ordered pair, (0, 0)

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Give the coordinates of each point:

Line Graphs

- Present a pictorial representation of the data you collected in your experiment
- Summarize how two pieces of information are related and how they vary depending on each other
- Scientists place
- The INDEPENDENT VARIABLE on the X AXIS, which is the HORIZONTAL AXIS.
- The DEPENDENT VARIABLE on the Y AXIS, which is the VERTICAL AXIS.

- What variable will be on the x axis?
- Independent Variable
- Time (minutes)

- Independent Variable
- What variable will be on the y axis?
- Dependent Variable
- Temperature (ºC)

- Dependent Variable

- Find the difference between the highest & lowest values for the variable.
- This is the range
- For Example:
- Highest Melting or Freezing Point: 93ºC
- Lowest Melting or Freezing Point: 32ºC
- Difference:61ºC This is your temperature range!

- Do the same for the other variable.
- For example:
- Longest time: 32 minutes
- Shortest time: 0 min (b/c we started @ 0)
- Difference: 32 minutesThis is your time range!

- B/c you graph paper is a rectangle, one side will be longer.
- You will need this side to be the axes with the largest range.
- Which range is higher, temperature or time?
- Temperature (61ºC) on the y axis

- Therefore, you will place your graph paper like thiswhen drawing your graph.

- Next, look to see if there are any negative numbers in your data.
- Since there aren’t any, your graph will be in which quadrant?
- Quadrant I

- Therefore, it will look like the letter “L”.

- Holding you paper like use a ruler to draw your x & y axis.
- Remember to indent 4 boxes from the bottom and 4 boxes from the left side so there is room for your labels.

- Go back and look at your ranges:
- Temp: 61ºC
- Time: 32 minutes

- Do you have 61 boxes on your y axis?
NO, how can you fit 61ºC on your paper?

- You can divide by 2 and have every box = 2ºC
- Or, you can divide by 5 and have every box = 5ºC

- Do you have 32 boxes on your y axis?
- YES, so 1 box = 1 minute

- Remember, you want you intervals to end in a 0 or 5.
- According to our example:
- If your lowest temperature is 32ºC & your highest is 93ºC, then you will need to start the y axis with 30ºC and go up 95ºC.
- Your x axis should start at 0 minutes and go up to 35 minutes

- Place tic marks and write you interval numbers

- Now you can plot your data points
- Use different colors to differentiate between your melting point and freezing point.
- I will be looking for the following:
- Title
- Correctly labeled x axis, including units
- Correctly labeled y axis, including units
- x axis correctly subdivided into scale
- y axis correctly subdivided into scale
- Data pairs correctly plotted
- Data trend summarized with line of best fit