2­2 Day 2 Linear Equations 2010 September 15, 2010
2.2 Linear Equations DAY 2
Objectives: Graph linear equations
and write equations of lines.
Jul 2­6:29 PM
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2­2 Day 2 Linear Equations 2010 September 15, 2010
Warm­up
Find the slope through each pair of points.
1. (­4, 8) and (5, 0)
2. (­1, ­3) and (0, ­8)
3. (0, ­7) and (2, ­1)
Jul 2­6:29 PM
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2­2 Day 2 Linear Equations 2010 September 15, 2010
Linear Function
• Graph is a line.
• Example: y = 3x + 2
• Solution: any ordered pair (x, y) that makes the equation true. • The value of y depends on the value of x.
• Therefore, y is the dependent variable and x is the independent variable.
Jul 2­6:29 PM
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2­2 Day 2 Linear Equations 2010 September 15, 2010
The y­intercept of a line is the point at which the line crosses the y­axis.
The x­intercept of a line is the point at which the line crosses the x­axis.
(0, y) y­intercept
(x, 0) x­intercept
Jul 2­6:29 PM
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2­2 Day 2 Linear Equations 2010 September 15, 2010
Graphing a Linear Equation
There are many ways to graph a line. Here is one method.
2
Graph the equation y = x + 3
3
Graph by plotting points.
x
y
­3
0
3
Jul 2­6:29 PM
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2­2 Day 2 Linear Equations 2010 September 15, 2010
Slope­Intercept Form:
y = mx + b
y = mx + b
slope y­intercept
Jul 14­4:47 PM
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2­2 Day 2 Linear Equations 2010 September 15, 2010
We have a formula for finding the slope of a line:
y2 ­ y1
Slope Formula: m =
x2 ­ x1
Example: Find the slope of the line through the points (3,2) and (­9,6).
Jul 2­6:29 PM
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2­2 Day 2 Linear Equations 2010 September 15, 2010
Graphing a Linear Equation
There are many ways to graph a line. Here is another method.
2
Graph the equation: y = x + 3
3
Graph by using slope­intercept form.
Slope­Intercept Form:
Slope:
y­intercept:
Sep 9­10:14 AM
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2­2 Day 2 Linear Equations 2010 September 15, 2010
Standard Form:
Ax + By = C
Ax + By = C
Positive Integer Integer
Integer
Jul 14­4:47 PM
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2­2 Day 2 Linear Equations 2010 September 15, 2010
Sep 15­10:20 AM
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2­2 Day 2 Linear Equations 2010 September 15, 2010
Graphing a Linear Equation
There are many ways to graph a line. Here is another method.
Graph the equation: 3x ­ 2y = 18.
Graph by finding intercepts.
x
y
Sep 9­10:14 AM
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2­2 Day 2 Linear Equations 2010 September 15, 2010
Example: Write in slope­intercept form to find the slope of 4x + 3y = 12 and graph the line.
Jul 14­4:47 PM
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2­2 Day 2 Linear Equations 2010 September 15, 2010
Name 4 ways to graph a linear equation:
1.
2.
3.
4.
Sep 15­9:15 AM
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2­2 Day 2 Linear Equations 2010 September 15, 2010
Example: The school glee club needs a total of $4500 for a trip to Omaha, Nebraska. To make money, members are selling baseball caps for $4.50 and sweatshirts for $12.50.
a. Graph the equation 4.5x + 12.5y = 4500, where x is the number of baseball caps and y is the number of sweatshirts sold.
b. Explain the meaning of the x­ and y­intercepts in terms of the fund­raising.
Sep 15­9:19 AM
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2­2 Day 2 Linear Equations 2010 September 15, 2010
Find the slope and write the equation of each line.
1.
2.
Sep 15­9:27 AM
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2­2 Day 2 Linear Equations 2010 September 15, 2010
HOMEWORK
page 67
(1 ­ 19 odd, 51 ­ 53, 66)
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