Activity 4. - Determining Slope Using The Slope Formula

 

Use the StraightLineEqn.xls tool, which displays a graph of an equation of the form:
y = mx + b.

 

              Δy                             change(y)                                 y2 – y1

Slope = ----    symbolically, ------------      or algebraically,    ---------

              Δx                             change(x)                                 x2 – x1

 

Where the left-most point is (x1 , y1) and the right-most point is (x2 , y2).

 

 

Do This.

Using the tool, first change the coefficient of x represented by “m” to .2 and the value of the constant term represented by “b” to 2. NOTE: To complete a change press the enter key after typing the new value.

 

Based on our discovery from Activity 2 and Activity 3, we know that the equation
y = 0.2x + 2 has a slope of .2

 

Enter 0 and 5 as x coordinates in the grid, respectively. The corresponding y coordinates are 2 and 3, as you can see on the grid and on the graph. The left end point of the line segment should therefore be (0, 2) and the right end point should be (5, 3). In this case, the left end point is (x1 , y1) and the right end point is (x2 , y2).

 

The left end point (0, 2) becomes (x1 , y1), where x1 = 0; y1 = 0

Similarly, right end point becomes (x2 , y2), where x2 = 0; y2 = 0

 

(a)                                                   y2 – y1

Use the formula: Slope =  ----------    and the two points (0, 2) and (5,3) to

                                                      x2 – x1

determine the slope of the line that passes through these two points. Show your work.

 

 

 

 

 

 

(b)      What answer were you expecting?  If you did not get the slope of the equation that equals the coefficient of x, then you made an error. Try again.

 

 

 

 

 

Just in case you still did not get it, let us do it together.

 

                           y2 – y1               3 - 2

Slope =  ----------      =  --------  =  0.2

                           x2 – x1              5 - 0

 

 

(c)      Working with a line segment with the end points of (-10, 0) and (10, 4), use the method shown in this activity to find the slope of the line segment between these points.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(d)      Use the same method to find the slope of the line segment between the end points
(-5, 1) and (5, 3).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(e)      Show that you understand the concept by explaining why the methods in Activities 3 and 4 are the same.

 

 

 

 

 

 

 

 

 

(f)      How many methods have we learned for finding the slope?

 

 

 

 

 

 

 

(g)      Name two benefits to being able to use several models for investigating the same inquiry.

 

 

 

 

TEACHER NOTES

 

This lesson incorporates the following teaching strategies bases on the NCTM standards.

 

In addition the lesson meets the following technology guidelines specified by Garofolo, Drier, Harper, Timmerman, and Shockey (2000):