Transcript Rectangular Coordinate System

Rectangular Coordinate System
Created by Laura Ralston
“A picture is worth a thousand words.”
• Graphs are widely used in the media. Newspapers
and magazines, television, reports to stockholders,
and newsletters all present information in the
form of a graph.
• Graphs are used so widely because they show a
lot of information in a form that makes it easy to
understand
Cartesian Coordinate System (Coordinate Plane or xy-plane)
y-axis
Quadrant
II
Quadrant I
Origin (0, 0)
Quadrant I I I
Quadrant I V
x-axis
Ordered pairs
• Because we have two number lines, we need
two numbers in order to find a solution.
• An ordered pair is a pair of numbers written
within parentheses in which ORDER matters.
(x , y)
• The first number in
the pair is called :
–
–
–
–
–
–
x-component
x-coordinate
independent variable
Abscissa
Input
It tells the number of
units to move on the xaxis; that is, right or
left.
• The second number in
the pair is called:
–
–
–
–
–
–
y-component
y-coordinate
dependent variable
Ordinate
Output
It tells the number of
units to move on the yaxis; that is up or down.
How to plot a point on the coordinate
plane?
• To “plot” a point, start at the origin.
• Move “x” units right (positive) or left (negative)
• Move “y” units up (positive) or down (negative)
http://www.youtube.com/watch?v=YlT726odQcM&
feature=related
Equations with two variables
• Will have a solution with two numbers
• Often expressed as an ordered pair
• Remember a solution makes the equation TRUE
http://www.youtube.com/watch?v=oYYoQvgGcMg
• To find a solution, we choose any number for
one of the variables (usually “x”). Substitute
into equation and solve for the other variable
(“y”)
Equations continued…..
• Because every real
number could be
selected for one
variable and would
lead to a real number
for the other variable,
an equation with two
variables has an
infinite number of
solutions
• The “graph” of an
equation gives us a
picture of the equation.
That is, it corresponds
to the set of points that
satisfy the equation
(make it true).
Graph of an Equation
• To graph an equation, we plot a number of
ordered pairs (usually 3 - must plot 2) that are
solutions to the equation.
http://www.youtube.com/watch?v=RSJqGZ8vlq
Q
• The points should appear to be in a straight
line. Therefore, they are called ….
Linear Equations in 2 Variables
• Standard Form
–
Ax + By = C where A, B, and C are real
numbers
• Variables on one side of equals sign in alphabetical
order
• No fractions or decimals for A, B, or C
• “A” must be positive
• No exponents of variables
Two points useful for graphing are
• X-intercept
– point where the line
crosses the x-axis
– at this point, y = 0
– Solve for x
• Y-intercept
– point where the line
crosses the y-axis
– at this point, x = 0
– Solve for y.
http://www.youtube.com/watch?v=EIbcD0Un1p8
Two special cases
• Horizontal Line
• Vertical Line
– has no x-intercept
– all ordered pairs have
the same y-coordinate
– has no y-intercept
– all ordered pairs have
the same x-coordinate
– y = b , where b is any
number
– x = k, where k is any
number