Activity 4. - Determining Slope Using The SlopeFormula

Use the StraightLineEqn.xls tool, which displays a graph ofan 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 xrepresented 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 newvalue.

Based on our discovery from Activity 2 and Activity 3, weknow 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 onthe 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 =  ----------    andthe two points (0, 2) and (5,3) to

x2  x1

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

(b)      Whatanswer were you expecting?  If you didnot get the slope of the equation that equals the coefficient of x, then you madean error. Try again.

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

y2  y1               3 - 2

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

x2  x1              5 - 0

(c)      Workingwith a line segment with the end points of (-10, 0) and (10, 4), use the methodshown in this activity to find the slope of the line segment between thesepoints.

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

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

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

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

TEACHER NOTES

This lesson incorporates the following teaching strategiesbases on the NCTM standards.

• Technology integration
• Interactive learning
• Concept-building through discovery
• Actively building new knowledge from experience and prior knowledge
• Discourse in mathematics
• Formulate explanations
• Mathematical literacy
• Using modeling to solve problems
• Making connections by investigating various models

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

• Applying technology to meaningful problems
• Employing technology to improve pedagogy
• Connect mathematical topics
• Use multiple representations