Specific Slopes

Problem Statement
How do the slopes of two parallel lines relate to each other?  Two perpendicular lines?

Problem setup

If two lines are parallel, and are graphed on the same coordinate plane, the slopes of the two lines will be the same. 


If two lines are perpendicular to each other, the slope of one line is the negative inverse of the other line.


Plans to Solve/Investigate the Problem

By graphing two parallel lines and finding the slope of each of the lines, we will show that the slopes are equal.


By graphing two equations – one perpendicular to the other – and finding the slope of each of the lines, we will show that the slope of one is the negative inverse of the other.


Investigation/Exploration of the Problem

Using the Graphing Calculator program on the computer, we went to Examples on the toolbar and then chose Learning Math.  We selected #1 “Slope-Intercept form” and graphed the basic formula for a line in slope-intercept form y = mx + b.  We found we could control the slope of the line “m” by moving the slider below the graph to the left and right.  By keeping the slope equal to 1 and changing the intercept “b” to 2, we graphed a second line with the same slope as the first line.  If we change “m” using the slider at the bottom, the lines could be rotated and would remain parallel since the slope is the same for both.






Next we used Geometer’s Sketchpad to construct two perpendicular lines and then measure the slopes of each.  We found that by rotating the figure, the slope of line j was the negative inverse of the slope of line k.


Click here to go to the Geometer’s Sketchpad file. 


Author & Contact
Jill Jackson and Shirley Crawford.
jjackson@rockdale.ga.us or scrawford@rockdale.ga.us 

Link(s) to resources, references, lesson plans, and/or other materials
Here is a link to another problem called “Late to School” which has practical application and may be of interest to middle school students.