Download y - cloudfront.net

exponent or power
WARM - UP strict inequality origin
variable
base
variable
1. A(n) __________
is letter used in algebra to represent any number from a given
Aug 24 - Wednesday
set of numbers.
origin
2. On the real number line, the real number zero is the coordinate of the ________.
strict inequality
3. An inequality of the form a > b is called a(n) ___________.
base
4. In the expression 24, the number 2 is called the _______
and 4 is called the
exponent or power
___________________.
True or False
1. The product of two negative real numbers is always greater than zero. True
2. The distance between two points on the real number line is always greater than zero. True
3. The absolute value of a real number is always greater than zero. False
4.To multiply two expressions having the same base, retain the base and multiply the exponents.
False
Section 1.1
The Distance and Midpoint
Formulas; Graphing Utilities;
Introduction to Graphing
Equations
•
(x, y)
Ordered pair
(x-coordinate, y-coordinate)
(abscissa, ordinate)
x axis
origin
Rectangular or Cartesian Coordinate System
Quadrant II
x < 0, y > 0
Quadrant I
x > 0, y > 0
Quadrant III
x < 0, y < 0
Quadrant IV
x > 0, y < 0
Let's plot the point (6,4)
Let's plot the point (-6,0)
(0,7)







(-6,0)
     

(-3,-5)
(6,4)
       






Let's plot the point (-3,-5)
Let's plot the point (0,7)
All graphing utilities (graphing calculators and computer
software graphing packages) graph equations by plotting
points on a screen.
The screen of a graphing utility will display the
coordinate axes of a rectangular coordinate system.
You must set the scale on each axis. You must also
include the smallest and largest values of x and y
that you want included in the graph. This is called
setting the viewing rectangle or viewing window.
Finding the Coordinates of a Point Shown on a
Graphing Utility Screen
Find the coordinates of the point shown. Assume the coordinates
are integers.
Viewing Window
2 ticks to the left on the horizontal axis (scale = 1)
and 1 tick up on the vertical axis (scale = 2), point is (–2, 2).
Find the midpoint of the line segment from P1 = (4, –2) to
P2 = (2, –5). Plot the points and their midpoint.
y
42
x
3
2
7
2  5

y
2
2
x
7

M   3,  
2






P1


M


P2

Determine if the following points are on the graph of the
equation –3x +y = 6
(a) (0, 4)
3  0  4  4  6
(b) (–2, 0)
(c) (–1, 3)
3  2  0  6
3  1  3  3  3  6












Graph Equations Using a Graphing Utility
To graph an equation in two variables x and y using a
graphing utility requires that the equation be written
in the form y = {expression in x}. If the original
equation is not in this form, rewrite it using equivalent
equations until the form y = {expression in x} is
obtained.
In general, there are four ways to obtain equivalent
equations.
Expressing an Equation in the Form
y = {expression in x}
Solve for y:
2y + 3x – 5 = 4
We replace the original equation by a
succession of equivalent equations.
Graphing an Equation Using a
Graphing Utility
Use a graphing utility to graph the equation:
6x2 + 2y = 36
Step 1: Solve for y.
6x  3y  36
2
3y  6x  36
2
y  2x  12
2
Exit Ticket:
1. Determine the distance between the points and .
2. Find the midpoint of the line segment joining the points and .
3. The graph of an equation is given. List the intercepts of the graph.
4. Graph 𝟐𝒙 − 𝟑𝒚 = 𝟔 using a graphing utility.