Transcript 2-2 Linear Equations

2-2 Linear Equations
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We will identify linear equations
and functions.
Linear Equations
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A linear equation has no operations other than
addition, subtraction, and multiplication of a
variable by a constant.
The variables cannot be multiplied together or
appear in the denominator.
Variables cannot have exponents other than 1.
And the graph of a linear equation is always a
line.
Equations
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Linear Equations
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Not Linear Equations
5x – 3y = 7
7a + 4b2 = -8
x=9
y=
6s = -3t – 15
x + xy = 1
y=½x
y = 1/x
x+5
Linear Functions
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A linear function is a function that can
be written in the form f(x) = mx + b,
where m and b are real numbers.
Ex.1 State whether each function
is a linear function. Explain.
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a) g(x) = 2x – 5
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b) p(x) = x3 + 2
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c) t(x) = 4 + 7x
Ex. 2 The linear function f(C) = 1.8C + 32 can be used
to find the number of degrees Fahrenheit, f, that
are equivalent to a given number of degrees
Celsius, C.
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h
a) On the Celsius scale, normal body
temperature is 37 degrees. What is the
normal body temperature in degrees
Fahrenheit?
Ex. 2 The linear functions f(C) = 1.8C + 32 can be used
to find the number of degrees Fahrenheit, f, that
are equivalent to a given number of degrees
Celsius, C.
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h
a) On the Celsius scale, normal body temperature is
37 degrees. What is the normal body temperature in
degrees Fahrenheit?
f(37)=1.8(37) + 32
=98.6 OF
Ex. 2 The linear functions f(C) = 1.8C + 32 can be used
to find the number of degrees Fahrenheit, f, that
are equivalent to a given number of degrees
Celsius, C.
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b) There are 100 Celsius degrees between the
freezing and boiling points of water and 180
Fahrenheit degrees between these two points. How
many Fahrenheit degrees equals 1 Celsius degree?
h
Ex. 2 The linear functions f(C) = 1.8C + 32 can be used
to find the number of degrees Fahrenheit, f, that
are equivalent to a given number of degrees
Celsius, C.
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h
b) There are 100 Celsius degrees between the
freezing and boiling points of water and 180
Fahrenheit degrees between these two points. How
many Fahrenheit degrees equals 1 Celsius degree?
If 100OC = 180OF…
then 1OC = 1.8OF
In lesson 2-1, we graphed an equation by
making a chart of values and then graphing
and connecting the ordered pairs.
Since 2 points determine a line, one way to
graph a linear equation or function in to
determine where it will cross each axis and
then connect those points. (Find the
intercepts.)