Geometry Quadrants – Coordinate Geometry

Points on a Grid

A location, or point, on a grid can be identified by an ordered pair such as (3, 2), which names the coordinates of that location or point. The first number tells how far to the right or left the point is located in the horizontal direction. The second number tells how far up or down the point is located in the vertical direction. Students must realize that, for example, that the point (3, 2) is not the same as point (2, 3). The numbers in an ordered pair are called coordinates.

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At this grade level, functions are graphed from tables of given values. All values are positive, thus the graphs of functions studied in this chapter are located in Quadrant I only. Formal definitions and extended work with functions are not necessary at this time.

A function is a rule that associates one and only one value of one variable with each value of another variable. The function y = 2x expresses y in terms of x. For each value of x, there is one and only one value of y. An equation determines y as a function of x, if for each x, the equation can be solved to give exactly one value of y. The graphs of such equations are lines in the plane. An equation that can be written Ax + By = C, where A, B, and C are fixed numbers, is called a linear equation.

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The graph of a linear equation is a straight line. To graph a linear equation, first a table of values for x and y is completed and then the ordered pairs are graphed. Finally a line is drawn through the points.

Equation: y = x + 3

These values can be interpreted as the x-coordinates and y-coordinates of points in the coordinate plane. Graphing these points means placing a dot at the points (–2, +1), (–1, +2), (0, +3), (+1, +4), and (+2, +5). To graph the equation, students connect the points with a straight line.

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