Review of the Cartesian Plane

You need to understand a graph before you can interpolate or extrapolate a graph on a Cartesian plane.  The Cartesian plane was introduced to mathematics by René Decartes (1596-1650).

Review the parts of the Cartesian Plane.

 

Modified Source:  NSU-Math 1030 Unit 4 Section 1

• Cartesian Plane - grid for identifying points on a plane using two axes
• x-axis - horizontal axis on the coordinate plane
• y-axis - vertical axis on the coordinate plane
• origin - the intersection point of the x- and y-axis.  It is usually the point (0, 0) on the cartesian plane.
• quadrants - one of the 4 regions formed by the x- and y-axis
• interpolate - to determine a data value on a curve between two known values
• extrapolate - to determine a data value by following a pattern outside of a curve of known values

Review Cartesian Coordinates

In the previous activity you reviewed the part of the grid or Cartesian Plane.  The plane is made up of points.  The x-axis (---) and y-axis ( | ) provide the location (coordinates) of each point.   Ordered pairs written (x,y) provide a simple way to write the location of each point on the plane.

source:  Simple Cartesian Coordinates

Move the mouse over the grid (white area) on the left.    Study the changes in the ordered pair name as you move your mouse.  What happens to the ordered pair as you move the mouse left, right, up, and down.    Check your responses by clicking on the buttons below.

Graphing Ordered Pairs

Instructions:

1. Take any ordered pair of the form (x, y). Example: (3, -4)
2. Use the mouse arrow to find that point on the graph.
3. Click on the point.
4. The coordinates you have clicked on will be given to you.
5. Did you find the point you were looking for?

source:  http://www.accessone.com/~bbunge

Locating Points

Click your mouse on the corresponding ordered pair on the graph.

source:  NSU-Math 1030 Unit 4 Section 2  Author

Your turn, find the solution in each of the following problems (note: some browsers don't update properly, if the point doesn't change you need to convince the browser to redraw everything, the easiest way is to scroll up until the picture is off the screen and then scroll down again):

source:  NSU-Math 1030 Unit 4 Section 1  Author

Now you are ready for two new games.  If you understand negative numbers, then the second game will be more challenging.

Interpolating and Extrapolating on the Cartesian Plane

Interpolation requires a set of data points: How much will the student make after: 3 hours?  5 hours?  Interpolation requires one to determine a data value on a curve between two known values. Positive Maze Game - Interpolate Quadrant I Maze Game - Interpolate - all Quadrants

Extrapolation requires a set of data points: If the temperature of the water continues at the same rate, how long will it take the water to reach: 80o?   100o?  Extrapolation requires one to determine a data value by following a pattern outside of a curve of known values.

Graphing a Line (y = mx + b)

Instructions:

1. Click "New Problem" to get an equation of the form y = mx + b.
2. Find the y-intercept on the graph. Click on that point. Keep trying until your answer is correct.
3. Using the slope (m), find any other point on the line. Click on that point. Keep trying until your answer is correct.
4. Any time you wish to see the line, click on "Draw the Line".
5. Can you find the correct points before you see the line?

source:  http://www.accessone.com/~bbunge

Graphing Helper for (y = mx + b)

Instructions:

1. This applet will help you graph equations of the form y = mx + b.
2. "m" is the slope of the line.
3. "b" is the y-intercept.
4. This program only works for integer values of m and b (no fractions or decimals - sorry!).
5. Type your values into the text fields. Then click on "Enter".

source:  http://www.accessone.com/~bbunge

Finding the Slope of a Line Segment

Instructions:

1. Click on a point.
2. Click on another point.
3. Drag the mouse between the points to make a line segment.
4. The coordinates of each endpoint are displayed at the right, along with the slope (m) of the line segment.
5. Can you calculate the slope without the computer's help?

Source:  http://www.accessone.com/~bbunge