Section 1.1:  Graphs and Graphing Utilities

The x-y coordinate system
The rectangular coordinate system
Cartesian coordinate system


Points and Ordered Pairs

Quadrants
Points correspond to ordered pairs of numbers

When we plot a point, we determine its location on the Cartesian grid.


Example 1.1.1
Plot the following points: (1, 3), (-2, 4), (-3, -3), (4, -3)



Graphs of Equations

A relationship between two quantities, x and y, is the equation in two variables.
Examples:

A solution of an equation in two variables is an ordered pair (x, y) such that when the x-coordinate and the y-coordinate are substituted into the equation, we get a true statement. We say that the ordered pair satisfies the equation.
Example 1.1.2


The graph of an equation in two variables is the set of all points whose coordinates satisfy the equation. To plot the graph, we usually plot a few individual points and then joined them with a smooth curve.

Graphing Equations and Creating Tales Using a Graphing Utility
The student should study this section independently.

Intercepts
x-intercept: the x-coordinate of the point where the graph intersects the x-axis. The y-coordinate is always zero.
y-intercept: the y-coordinate of the point where the graph intersects the y-axis. The x-coordinate is always zero.
A graph may have no intercepts or several intercepts.

R1C2 R1C3
2 intercepts 0 intercepts several intercepts

Interpreting Information Given by Graphs

You need to know what the axes represent and the scale been used.  Then find the appropriate value on the axis, moved out to the curve parallel to the other axis, and then move parallel to the original axis until you come to the other axis. The value there corresponds to the other value of the ordered pair.
Example 1.1.3 - Problem 64/93

  1. What is the head circumference at birth?  35 cm
  2. What is the head circumference at 9 months?  47 cm
  3. What is the head circumference at 14 months?  50 cm