Transcript Section 01

Chapter 7 Section 1
The Cartesian Coordinate
System and Linear Equations
in Two Variables
Learning Objective
• Plot points in the Cartesian (Rectangular) Coordinate
System.
• Determine whether an ordered pair is a solution to a
linear equation.
• Key Vocabulary: graph, Cartesian coordinate system,
rectangular coordinate system, quadrants, x-axis, yaxis, origin, coordinates, ordered pairs, linear
equation in two variables, collinear
Plot Points in the
Cartesian (Rectangular) Coordinate System
• A graph shows the relationship between two
variables in an equation.
• Ordered pairs are the x- and y-coordinates of
a point are placed in parentheses, with the xcoordinate listed first.
Plot Points in the Cartesian (Rectangular)
Coordinate System
The two intersecting axes form four quadrants that are numbered
I, II, III and IV. Origin is where the x and y axes intersect
y-axis - vertical
Positive
II
I
Origin
x-axis
horizontal
(0,0)
Negative
III
IV
Plot Points in the Cartesian (Rectangular)
Coordinate System
Example:
A
Plot each point
on the same axes.
B
D
A(4,4)
B(-2,3)
F
(0,0)
C(-4,-2)
D(0,2)
E(2,-2)
F(-3,0)
C
E
Plot Points in the Cartesian (Rectangular)
Coordinate System
Example:
List the ordered
pairs for each
point.
F
A
A = (3,2)
B = (0,-3)
D
(0,0)
C = (-2,-2)
D = (-1,0)
E = (2,-4)
F = (-4,2)
C
B
E
Determine whether an Ordered Pair is a
Solution to a Linear Equation
• A linear equation in two variables is an equation that can be
put in the form, ax + by = c, where a, b, and c are real
numbers.
• The graphs of equations of the form ax + by = c are straight
lines. This is why they are called linear.
• The adjective straight is not needed to describe lines. All lines
are straight. It is used to emphasize the shape of the graph.
• A set of point that are in a straight line are said to be
collinear.
Determine whether an Ordered Pair is a
Solution to a Linear Equation
Example:
(2,4)
Determine
whether the three
points appear to
be collinear.
(-1,-5)
(0,0)
(0,-2)
(2,4)
(0,-2)
Yes the line is
collinear.
(-1.-5)
Determine whether an Ordered Pair is a
Solution to a Linear Equation
Example:
(2,4)
Determine
whether the three
points appear to
be collinear.
(-2.1)
(-3,-2)
(0,0)
(-2,1)
(2,4)
No, the line is not
collinear.
(-3,-2)
Determine whether an Ordered Pair is a
Solution to a Linear Equation
Example:
Determine which of the following ordered pairs satisfy the equation.
x + 2y = 7
(3,2), (4,-1), (-1,4), (-3,5)
x + 2y = 7
x + 2y = 7
x + 2y = 7
x + 2y = 7
3 + 2(2) = 7
4 + 2(-1) = 7
-1 + 2(4) = 7
-3 + 2(5) = 7
3+4=7
4 + -2 = 7
-1 + 8 = 7
-3 + 10 = 7
7=7
2≠7
7=7
7=7
TRUE
FALSE
TRUE
TRUE
Determine whether an Ordered Pair is a
Solution to a Linear Equation
(-3,5)
Example:
(-1,4)
.
x + 2y = 7
(3,2) True
(4,-1) False
(-1,4) True
(-3,5) True
(3,2)
(0,0)
(4.-1)
Remember
• With ordered pairs the order does matter. x is always first.
(x, y)
• We graph solutions to linear equations in one variable on a
number line to give a visual representation of the solution
set.
• We graph solutions to linear equations in two variables
using ordered pairs in the Cartesian (rectangular) plane to
give a visual representation of the solution set.
• Two distinct points completely determine a line.
HOMEWORK 7.1
Page 429-430:
#27, 29, 37, 39