1.4 Linear Functions 2011 September 02, 2011
1.4 ‐ Linear Functions
Objectives:
• Review the midpoint and distance formulas.
• Graph linear functions that are written in slope­intercept form and standard form.
• Write the equation of a line given specific properties.
• Graph lines written in standard form using the intercepts.
• Use linear functions to solve problems.
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1.4 Linear Functions 2011 September 02, 2011
The Midpoint Formula
The Distance Formula
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1.4 Linear Functions 2011 Example:
September 02, 2011
Find the midpoint and distance between the points (­4, 7) and (11, ­3).
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1.4 Linear Functions 2011 September 02, 2011
Example:
• Find the slope.
(2, 3)
(­1, ­5)
•
Write the equation of the line.
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1.4 Linear Functions 2011 September 02, 2011
Point­Slope Formula
y ­ y1 = m(x ­ x1)
Slope­Intercept form
y = mx + b
Standard Form
Ax + By = C
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1.4 Linear Functions 2011 September 02, 2011
Writing Equations of Lines
Point­Slope Formula
y ­ y1 = m(x ­ x1)
1. Write the equation of the line given m = ­2 and the point (­2, 3). 6
1.4 Linear Functions 2011 September 02, 2011
Writing Equations of Lines
2. Write the equation of the line given the points (2, 3) and (­4, 5). 7
1.4 Linear Functions 2011 September 02, 2011
Writing Equations of Lines
3. Find the equation of the line that contains the point
(1, ­2) and is perpendicular to the line x + 2y = 6.
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1.4 Linear Functions 2011 September 02, 2011
Writing Equations of Lines
4. Find the equation of the line that contains the point
(2, ­3) and is parallel to the line 2x + y = 6.
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1.4 Linear Functions 2011 September 02, 2011
5. Show that the two lines are parallel.
2x + 3y = 6
4x + 6y = 0
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1.4 Linear Functions 2011 September 02, 2011
6. Find the intercepts of the graph and then graph the line.
2x + 4y = 8
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1.4 Linear Functions 2011 September 02, 2011
Application problem
7. Commonwealth Edison Company supplies electricity to residential customers for a monthly charge of $7.58 plus 8.275 cents per kilowatt­hour for up to 400 kilowatt­hours.
a. Identify the variables. State the domain of the function.
b. Write an equation that relates the monthly charge, in dollars,
to the number of kilowatt­hours used in a month. c. What is the monthly charge for using 100 kilowatt­hours?
d. What is the charge for using 300 kilowatt­hours?
e. Describe what the y­intercept represents and what the slope represents.
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1.4 Linear Functions 2011 September 02, 2011
Homework
page 9 (40, 62, 66, 68)
&
page 41 (33, 35, 44­64 even, 90­96 even, 105, 120)
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