Conclusion

This chapter has provided a context in which you have explored several types of work related to linear equations. Exploring how to calculate slopes allowed you to gain a stronger sense of the way that coordinate pairs relate to each other. You extended this understanding to encompass use of the Pythagorean theorem, which allowed you to calculate the distances separating points on a line. From there, you moved on to investigate the slopes of lines and their inverses, which enabled you to find perpendicular lines.

You also worked with such things as translation of lines and symmetry, and these activities will prove important as you move on to work with quadratic and other equations. When you explored absolute values, you were able to generate symmetrical lines by mirroring positive and negative values. In your explorations of symmetry relative to points, axes, and lines, you saw that if you generate values that are the square of x, you arrive at a line that is symmetrical to the y axis. If you generate values that are the cube of x, you arrive at a line that is symmetrical to the origin of the Cartesian plane. Still other lines are symmetrical to the line you create with the equation x = y.