2­2 Day 1 Linear Equations 2009
September 10, 2009
2.2 Linear Equations
Objectives: Graph linear equations
and write equations of lines.
Jul 2­6:29 PM
1
2­2 Day 1 Linear Equations 2009
September 10, 2009
Warm­up
Evaluate each expression for x = ­2.
2
1. x + 7
3
3
2. x ­ 2
5
3. 3x + 1
1
4. x ­ 8
2
Simplify.
1
5. (x + 4)
2
1
6. ­ (x ­ 10)
2
1
7. (x + 12)
3
Jul 2­6:29 PM
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2­2 Day 1 Linear Equations 2009
September 10, 2009
Linear Function
• Graph is a line.
• Example: y = 3x + 2
• Solution: any ordered pair (x, y) that makes the equation true. (any point on the line)
• The value of y depends on the value of x.
• Therefore, y is the dependent variable and x is the independent variable.
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2­2 Day 1 Linear Equations 2009
September 10, 2009
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 1 Linear Equations 2009
September 10, 2009
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 1 Linear Equations 2009
September 10, 2009
Slope­Intercept Form:
y = mx + b
y = mx + b
slope y­intercept
Jul 14­4:47 PM
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2­2 Day 1 Linear Equations 2009
September 10, 2009
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
7
2­2 Day 1 Linear Equations 2009
September 10, 2009
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
8
2­2 Day 1 Linear Equations 2009
September 10, 2009
Standard Form:
Ax + By = C
Ax + By = C
Positive Integer Integer
Integer
Jul 14­4:47 PM
9
2­2 Day 1 Linear Equations 2009
September 10, 2009
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
10
2­2 Day 1 Linear Equations 2009
September 10, 2009
Example: Write in slope­intercept form to find the slope of 4x + 3y = 12 and graph the line.
Jul 14­4:47 PM
11
2­2 Day 1 Linear Equations 2009
September 10, 2009
HOMEWORK
page 67
(2 ­ 18 even, 32 ­ 34, 42 ­ 47, 52 ­ 64 even)
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