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Middle/High School Algebra, Geometry, and Statistics (AGS)
1.14 Graphs for Constant Coordinates

Plot the following point on a graph sheet
(2,1),(2,2),(2,3),(2,4),(2,5),(2,0),(2,-1),(2,-2),(2,-3),(2,-4) and (2,-5).

Observing the above graph:

1. All these points lie on a straight line which is perpendicular to X-axis.
2. All these points lie on a straight line which is parallel to Y-axis.
3. The x-coordinate is constant for all these points.  That is x = 2.
4. The common property of all these points on the straight line is x = 2.
5. x = 2 is a straight line parallel to Y-axis and at a distance of 2 units right and it intersects the X-axis at the point (2,0).
x = 2 is a relation and this is satisfied by all those ordered pairs in which the first coordinate x is always 2 and the second coordinate y is any real number.

Draw the graph of y = 3.
All the points whose second coordinate y is 3 and whose first coordinate is any real number satisfy this relation.  Some ordered pairs that satisfy the given relation are (0,3),(1,3),(3,3),(4,3),(-1,3),(-2,3),(-3,3) and (-4,3).

Observing above graph, all these ordered pairs when plotted lie on a straight line which is parallel to the X-axis.  The straight line y=3 is parallel to X-axis and it intersects Y-axis at the point (0,3).

Directions: Draw the graph for linear equations. Verify using TI 83 or TI 84 graphing calculator.
x = 1
x = 2
x = 3
x = 4
y = 1
y = 2
y = 3
y = 4