Lines are where we begin. We take the notion of a straight line as being the objects that, given two destinations on the line (points), the shortest path between those those two points lies entirely on the line. This is the human centered approach because we innately have a sense of distance. We know from walking along paths which path is shorter. Using distance as our guide, we use that to define lines, triangle, circles, and angles. Once we have those, we can construct a coordinate system. This system gives us a means of plotting and visualizing the objects we will be talking about. With the right tools in place, we can then define slopes of straight lines, something which is often assumed in the standard treatment of textbooks. We will take some time to learn how to solve linear equations, a crucial topic to be comfortable with. We will look at various techniques to do so. We apply those techniques to the particular cases of perpendicular and parallel lines. We conclude with revisiting the solution techniques in the situation of linear inequalities which we solve in similar fashions with a few twists.
In this section, we build up the core tool in defining lines: the notion of distance.
What are lines, circles, angles, and triangles?
Grids, grids, everywhere there's grids.
This hill is steep! What does that mean? Let's talk slope.
Let's solve some linear equations. It will be fun!
Lines that never meet? Lines that make corners?
Inequalities are notoriously difficult. But we can tackle them almost the same way as we tackle solving a line. We just have to be mindful of direction.