Linear+Equations

=Linear Equations=

[[image:2010-04-18_1924.png width="480" height="311" align="right" link="@http://www.box.net/shared/cqz1rj9ixd"]]Example #1: Linear Equations
This example is designed for student creation. Teacher would provide a blank template so that students would not have to figure out how to graph in Excel all three graphs on the same worksheet (use control button to highlight each set of cells needed to graph all three lines at the same time).

Use this exercise to investigate linear equations in the slope-intercept form of **y=mx+b** (where m is the slope and b is the y-intercept.)

1) Students use what they know about graphing linear equations (table method) and enter a values for x and y for their choice of a linear equation.

(Note: I am not using excels formulas to do this - students are inputting the numbers from their calculations on paper or on a calculator.)

As the values are entered in, the graph is drawn (we are using a scatterplot).

2) Students then choose another linear equation, this time with the same slope (m=2) with a different b. Students enter a table of values for this equation and analyze the results (students should see in the graph that the lines look parallel).

3) Students are then asked to create a table of values for an equation where they use the negative reciprocal for m (in this case, -1/2) and any b.

When they enter in these values, students will see that the new graph intersects the other two graphs...this graph is also perpendicular to the other two graphs.

Through this exercise students have verified the relationships between the slopes of parallel and perpendicular lines.
 * slopes of parallel lines are the same (will never intersect)
 * lines with different slopes intersect
 * slopes that are negative reciprocals of each other are perpendicular (form right angles) with each other

Example #2: Linear Equations
//from Scott Sinex: Developer's Guide to Excelets http://academic.pgcc.edu/~ssinex/excelets///

In this pre-made interactive spreadsheet, students can use the worksheet to "play" with the numbers of a linear equation.

The slope and y-intercept of two lines can be changed. The excelet returns the graphs of the two equations, their intersection point, etc.

The comments sections give students information about parallel and perpendicular lines. Students can also interact with vertical lines on the graph and see that vertical lines have an //undefined slope.// If slope = 0, the line is horizontal.

This spreadsheet also allows users to interact with straight lines to form quadrilaterals and three ways to plot lines using two points, a point and the slope and the slope-intercept method (see the tabs at the bottom of the page).

This interactive could be used in a lab setting where students would interact with activity and work through some __good__ questions:
 * If I change the intercept, how does that graph change?
 * If I change the slope to negative, how does the graph change?
 * How do I know whether or not the lines will intersect?
 * How do I know whether or not the lines will not intersect?
 * How can I create two intersecting lines that are perpendicular?

__Extension: Determine x and y Intercept__[[image:2010-04-20_0715.png width="456" height="272" align="right" link="@http://www.box.net/shared/3sa1svigfd"]]
from Scott Sinex: Developer's Guide to Excelets //http://academic.pgcc.edu/~ssinex/excelets///

Use this interactive spreadsheet to explore the x and y intercepts of a linear equations. I often concentrate on the y-intercept (b) but this worksheet extends the learning even further to help students to see x-intercept and how to find it!

**Simultaneous Equations**
//Use this interactive excel spreadsheet to help students understand the graphical solutions of simultaneous equations.//

from Flexcel - Flexible Interactive Workbooks in Excel http://www.maths-it.org.uk/Flexcel/Flexcel.php by Rob Simpson

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 * //Pages Created by Kathleen L Post//**