Transcript HA2 Linear Equations - Appoquinimink High School

September 17, 2010
Objectives
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Students will be able to:
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Identify linear equations and functions,
Write linear equations in standard form
and graph them.
Key Words
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Linear Equations:
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Linear Function:
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Has no operations other than addition,
subtraction, and multiplication of a variable by a
constant.
Is a function whose ordered pairs satisfy a linear
equation.
Standard Form:
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Ax + By = C
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Y-Intercept:
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The y value when x = 0.
X-Intercept:
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The x value when y = 0.
State whether
Explain.
is a linear function.
Answer: This is a linear function because it is in the form
State whether
Explain.
is a linear function.
Answer: This is not a linear function because x has an
exponent other than 1.
State whether
Explain.
is a linear function.
Answer: This is a linear function because it can be written
as
State whether each function is a linear function.
Explain.
a.
Answer: yes;
b.
Answer: No; x has an exponent
other than 1.
c.
Answer: No; two variables are
multiplied together.
Meteorology The linear function
can be used to find the number of degrees Fahrenheit,
f (C), that are equivalent to a given number of degrees
Celsius, C.
On the Celsius scale, normal body temperature is
37C. What is normal body temperature in degrees
Fahrenheit?
Original function
Substitute.
Simplify.
Answer: Normal body temperature, in degrees
Fahrenheit, is 98.6F.
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 equal 1 Celsius degree?
Divide 180 Fahrenheit degrees by 100 Celsius degrees.
Answer: 1.8F = 1C
Meteorology The linear function
can be
used to find the distance d(s) in miles from a storm,
based on the number of seconds s that it takes to
hear thunder after seeing lightning.
a. If you hear thunder 10 seconds after seeing lightning,
how far away is the storm?
Answer: 2 miles
b. If the storm is 3 miles away, how long will it take to
hear thunder after seeing lightning?
Answer: 15 seconds
Write
in standard form. Identify A, B, and C.
Original equation
Subtract 3x from each side.
Multiply each side by –1 so
that A  0.
Answer:
and
Write
and C.
in standard form. Identify A, B,
Original equation
Subtract 2y from each side.
Multiply each side by –3 so that
the coefficients are all integers.
Answer:
and
Write
and C.
in standard form. Identify A, B,
Original equation
Subtract 4 from each side.
Divide each side by 2 so that the
coefficients have a GCF of 1.
Answer:
and
Write each equation in standard form. Identify A, B,
and C.
a.
Answer:
and
b.
Answer:
and
c.
Answer:
and
Find the x-intercept and the y-intercept of the graph of
Then graph the equation.
The x-intercept is the value of x when
Original equation
Substitute 0 for y.
Add 4 to each side.
Divide each side by –2.
The x-intercept is –2. The graph crosses the
x-axis at (–2, 0).
Likewise, the y-intercept is the value of y when
Original equation
Substitute 0 for x.
Add 4 to each side.
The y-intercept is 4. The graph crosses the y-axis at (0, 4).
Use the ordered pairs to graph this equation.
Answer: The x-intercept is –2, and the y-intercept is 4.
(0, 4)
(–2, 0)
Find the x-intercept and the y-intercept of the graph of
Then graph the equation.
Answer: The x-intercept is –2, and the y-intercept is 6.
Homework
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Page 110 (41-46,48-50,54,66,70-72)