3.6 Lines in the Coordinate Plane
October 19, 2009
3.6 Lines in the Coordinate Plane
Objectives:
Graph lines given their equations.
Write equations of lines.
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3.6 Lines in the Coordinate Plane
October 19, 2009
Review: Here is a formula for finding the slope of a line.
Slope Formula:
m =
y2 ­ y1
x2 ­ x1
Example: Find the slope of the line through the points (3,2) and (­9,6).
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3.6 Lines in the Coordinate Plane
October 19, 2009
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3.6 Lines in the Coordinate Plane
October 19, 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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3.6 Lines in the Coordinate Plane
October 19, 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
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3.6 Lines in the Coordinate Plane
October 19, 2009
Graphing a Linear Equation
There are many ways to graph a line. Here is one method.
Example #1:
2
Graph the equation y = x + 3
3
Graph by plotting points.
x
y
­3
0
3
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3.6 Lines in the Coordinate Plane
October 19, 2009
Slope­Intercept Form:
y = mx + b
y = mx + b
slope y­intercept
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3.6 Lines in the Coordinate Plane
October 19, 2009
Graphing a Linear Equation
There are many ways to graph a line. Here is another method.
Example #2:
1
Graph the equation: y = x ­ 5
4
Graph by using slope­intercept form.
Slope­Intercept Form:
Slope:
y­intercept:
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3.6 Lines in the Coordinate Plane
October 19, 2009
Example #3:
2
Graph the equation: y = ­ x ­ 3
5
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3.6 Lines in the Coordinate Plane
October 19, 2009
Standard Form:
Ax + By = C
Ax + By = C
Positive Integer Integer
Integer
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3.6 Lines in the Coordinate Plane
October 19, 2009
Graphing a Linear Equation
There are many ways to graph a line. Here is another method.
Example #4:
Graph the equation: 3x ­ 2y = 18.
Graph by finding intercepts.
x
y
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3.6 Lines in the Coordinate Plane
October 19, 2009
Example #5: Write in slope­intercept form to find the slope of 4x + 3y = 12 and graph the line.
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3.6 Lines in the Coordinate Plane
October 19, 2009
Example #6: Write in slope­intercept form to find the slope of ­5x + y = ­3 and graph the line.
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3.6 Lines in the Coordinate Plane
October 19, 2009
Point-Slope Form:
The line through point (x1, y1) with
slope m has the equation:
y - y1 = m(x - x1)
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3.6 Lines in the Coordinate Plane
October 19, 2009
Example #7: Write in point­slope form 1
an equation of the line with slope ­ 2 through the point (8, ­1).
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3.6 Lines in the Coordinate Plane
October 19, 2009
Example #8: Write in point­slope form the equation of the line through (1, 5) and (4, ­1).
y ­ 5 = ­2(x ­ 1)
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3.6 Lines in the Coordinate Plane
October 19, 2009
Attention:
The slopes of
horizontal and
vertical lines
have special
properties.
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3.6 Lines in the Coordinate Plane
October 19, 2009
Horizontal Line:
y=b
m=0
y is constant
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3.6 Lines in the Coordinate Plane
October 19, 2009
Vertical Line:
x=c
m is undefined
x is constant
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3.6 Lines in the Coordinate Plane
October 19, 2009
Example #9: Write the equations of the horizontal and vertical lines that contain the point P(5, ­1).
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3.6 Lines in the Coordinate Plane
October 19, 2009
Homework:
page 169 (1 ­ 4, 11 ­ 37 odd)
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