Transcript Review of Linear Functions & 1.2 Introduction to the TI

Chapter 1: Linear Functions
V. J. Motto
M110 Modeling with Elementary Functions
1.1 Review of Linear Functions
1.2 Introduction to TI-83+
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Housekeeping
Essay Assignment
 Getting Help

Come visit me!
 Mathematics Laboratory Dana 208
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Office Hours
MWF 1000 – 1100 Room Dana 220/208
 MWF 1330 – 1400 Room UT 306, Dana
220 or Dana 208
 By Appointment
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Rectangular Coordinate System
Note the x-axis and
y-axis. The cross
at the point (0, 0)
or the Origin.
There are 4
quadrants
numbered counter
clockwise with
Roman Numerals.
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Coordinates (x, y)
To plot or graph
the point that
corresponding to
the ordered pair
(a, b) we start at
the origin and
move a units left
or right. Then
we move b units
up or down.
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Graphing y = - 300x + 2000
Value (dollars)
Computer Value
2500
2000
1500
1000
500
0
Series1
0
2
4
6
Time (years)
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Example: Graphing y = 3x - 5
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Lets use our TI-83+
to sketch the graph
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y = button
Graph button
2nd Graph Table
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Linear Equations
A linear equation in two variables is an equation
that can be written in the form
Ax + By = C
Where A, B, and C are real numbers and A and
B are not both 0. The graph of a linear
equation in two variable is a straight line.
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Comment
Often, it is more convenient to solve the equation for y.
Thus, the linear equation
3x + y = 4
would be manipulate to become
y = - 3x + 4
which is easier to use when creating tables. You
choose different x values and calculate the
corresponding y values.
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Example: Graphing – 5x + 3y = 15
5 x  3 y  15
3 y  5 x  15
5
y  x 5
3
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Forms of Linear Equations
Form
Ax + By = C
y = mx + b
y – y1 = m(x - x1)
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Description
Standard Form.
A and B are not both 0
Slope-intercept Form.
Slope is m; y-intercept is (0, b)
Point-slope Form
Slope is m; (x1, y1) is a point of the line
y=c
Horizontal Line
Slope is 0; y-intercept is (0, c)
x=c
Vertical Line
Slope is undefined; x-intercepet is (c, 0)
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