Lines Part I

Being able to work with lines is basic to calculus. You are probably already familiar with plotting points on the cartesian plane. Let's take some time to review.

All points on the cartesian coordinate system consist of two values represented together as (x,y). The x represents the horizontal distance from the point (0,0) which may be positive(right) or negative(left). The y represents the vertical distance from (0,0) which may be positive(up) or negative(down). Take for instance the point (-2,3):


The x is negative so horizontally we go left 2 units. The y is positive so we go up 3 units.

In addition to points, we can represent lines using basic algebra. Lines are represented using the variables x and y(also z if plotting in 3-D), some numbers, and an (in)equality sign. We can represent a simple vertical line with the equation x = 2. That means in coordinates for every y value there is an x value of 2 such as the points (2,-2), (2,-1), (2,0), and (2,1), and all the points in between. Graphed it looks like this:


We can also have an equation with only a y variable such as y = -3. That means every x coordinate has a corresponding y value of -3 which looks like this: