- Sarah Keistler
To observe the relationships between parallel lines, I first constructed three sets of parallel lines. First using the point tool I plotted two points on the coordinate plane and constructed a line using the line tool that went through each of the two points. Then I plotted another point not on the line. Using the parallel line tool, I constructed a parallel line with the line and point. Then I measured the slope with the slope tool. I also wanted to see the equation of the line. So from the Algebra section, the equation of the line was already calculated and I simply drug the equation out to view it on the coordinate plane. I did this three different times to construct the above sets of lines. Once the lines were constructed I was able to see the similarities and differences in the lines. For example lines A and B both have a slope of which we can see from the slope calculated and the equation which is in format. From this format we know that m represents the slope and b represents the y-intercept of the line. I also observed that lines A and B had different y-intercepts. A had an intercept of 0 and B had an intercept of -2. I observed the same patterns for lines C and D and E and F. For lines C and D they both had a slope of -4. C had a y-intercept of 52 and D was 60. For lines E and F I observed that they both had a slope of 0.13. E had a y-intercept of of -2.77 and F of -3.64. From these three sets of parallel lines we can make the conjecture that for two lines to be parallel they must have the same slope and different y-intercepts. When this occurs then the lines will continue on infinitely without ever intersecting.