Graphing in the Coordinate Plane

1
Chapter 3.1

• Graphing in the Coordinate Plane
• (Midpoint and Distance Formula Optional)

2
Ordered Pairs

• To graph ordered pairs of real numbers, we need a
  new coordinate system. The rectangular or
  Cartesian coordinate system consists of a
  horizontal number line, the x-axis and a vertical
  number line, the y-axis as shown in the next
  slide.

3
y
P (a,b)
y - axis
Quadrant I
Quadrant II
Origin
x

Quadrant IV
Quadrant III
x - axis
4
y

Locate on the xy-plane the point corresponding to
the ordered pair (2,3) (-2,-3) (-1,3)
(0,-4) (4,-2)
x

5
Ordered Pairs

• An equation in two variables, such as y 2x3,
  is satisfied only if we find a value for x and a
  value for y that makes it true.

6
Ordered Pairs

• 2x 3y 6
• For example, if x 6 and y -2, then the
  equation becomes

7
Ordered Pairs

• The order of the numbers in an ordered pair is
  important. For example, (3,0) also satisfies
• 2x 3y 6

8
Ordered Pairs

• 2x 3y 6
• However, (5,1) does not.
• In the ordered pair, the value for x is always
  written first and the value for y second (x,y)

9
y
Graphing a Linear Equation
Graph 2x 3y 6
x

10
Linear Equation in Two Variables

• A linear equation in two variables can be written
  in the form
• Ax By C
• where A, B, and C are real numbers.
• this form is called standard form.

11
y

Graph 4x - y -3 Use x and y intercepts.
x

12
y

Graph y 2
x

13
y

Graph x1 0
x

14
y

Use Intercepts to Graph x 2y 4
x

15
Linear Equation in Two Variables

• L 3.1 1 - 50