Patterns on the Map: Graphing Relationships

To map a pattern, we use a coordinate plane. This is a flat surface formed by two intersecting lines: the x-axis (horizontal) and the y-axis (vertical). Every location on this map is called an ordered pair, written as $(x, y)$. The first number, $x$, tells you how far to move across from the origin $(0, 0)$. The second number, $y$, tells you how far to move up. Think of it like an elevator: you have to walk across the lobby before you can go up to your floor!

Often, math gives us a rule that creates a pattern. For example, 'Multiply the input by 2 to get the output.' We can turn this into a table of values. If our input ($x$) is $1$, our output ($y$) is $2$. If $x$ is $2$, $y$ is $4$. These pairs $(1, 2)$ and $(2, 4)$ are coordinates! When we graph multiple points from the same rule, they often form a straight line, showing us a linear relationship.

Once your points are on the graph, look at the direction. If the points go up as you move from left to right, the relationship is increasing. This might represent a plant growing over time. If the points go down, the relationship is decreasing, like the amount of water left in a leaking bucket. Graphs allow us to see the 'big picture' of data at a single glance.