For each value of x, there is one and only one value of y: For example, the function y = 2 x expresses y in terms of x. Formal definitions and extended work with functions are usually not taught until at least Grade 8.Ī function is a rule that associates one and only one value of one variable with each value of another variable. All values are positive, thus the graphs of functions studied in this chapter are in Quadrant I only. To locate (3,2), move 3 units to the right on the x-axis and 2 units up on the y-axis.Īround Grade 5, functions are graphed from tables of given values. The location of (3,2) is shown on the coordinate plane below. Note that coordinates are often written with no space after the comma. Ordered pairs are written in parentheses ( x-coordinate, y-coordinate). Each point can be identified by an ordered pair of numbers that is, a number on the x-axis called an x-coordinate, and a number on the y-axis called a y-coordinate. The numbers on a coordinate plane are used to locate points. The point where the x- and y-axis intersect is called the origin. The vertical axis is usually called the y-axis. The horizontal axis is usually called the x-axis. With the extension of the number system to include negative numbers, each axis can be extended in two directions. A coordinate plane has two perpendicular lines, or axes (pronounced AK-seez), labeled just like number lines. The relationships are shown on a coordinate plane. Note how numbers such as −3 and +3 are opposite numbers.Ĭoordinate graphing is a visual method for showing relationships between numbers. The positive integers are represented to the right of 0 and the negative integers are represented to the left of 0. Representing the concept of being opposite using a negative sign lets us represent all the integers on a number line that extends both to the left and to the right of zero. There is nothing stopping you from representing a $5 debt by representing "$5" using red text instead of black or adding the word "owed" next to it. Notice how mathematics rarely presents just one model for the real world. However, humans have long had some conception of negative numbers, due to phenomena such as measuring sea level or debt. Historically, negative numbers largely came about as a way of solving equations that otherwise wouldn't have solutions, such as x + 8 = 3. Notice that 0 is the only number whose opposite is itself. The integer numbers (or simply integers) extend whole numbers to their opposites. If we start counting from 0 instead, the set of numbers are instead called whole numbers. These are the counting numbers that start with 1, 2, and 3, and go on forever. The most common numbers that we encounter-in everything from speed limits to serial numbers-are natural numbers. The numbers in an ordered pair are called coordinates. Note that the point (3,2) is not the same as point (2,3). The second number tells how far up or down the point is located in the vertical direction. The first number tells how far to the right or left the point is located in the horizontal direction. ( Common Core 6.NS.C.8, Florida BEST MA.6.GR.1.1)Ī location, or point, on a grid can be identified by an ordered pair such as (3,2), which names the coordinates of that point.
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