welcome to the mm204 unit 7 seminar
DESCRIPTION
Welcome to the MM204 Unit 7 Seminar. Section 4.1: The Rectangular Coordinate System. Origin Plot: (2, 5) (-3, 4) (1, -6). Section 4.1. Standard Form of an Equation Ax + By = C If a letter is missing, that means a or b must be zero. Examples: 2x + 3y = -73x – 5y = 8 - PowerPoint PPT PresentationTRANSCRIPT
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WELCOME TO THE MM204
UNIT 7 SEMINAR
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Section 4.1: The Rectangular Coordinate System
Origin
Plot:
(2, 5)
(-3, 4)
(1, -6)
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Section 4.1
Standard Form of an Equation Ax + By = C If a letter is missing, that means a or b must
be zero.
Examples:
2x + 3y = -7 3x – 5y = 8
a = 2 a = 3
b = 3 b = -5
c = -7 c = 8
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Section 4.1
A Solution to an Equation A solution is a point on the line when
graphed. Without graphing, a solution makes the
statement true. Example: Is (-1, 1) a solution to 2x – 3y = -5?
2(-1) – 3(1) = -5 Plug in the point.
-2 – 3 = -5 Simplify.
-5 = -5 True Statement.
Yes, (-1, 1) is a solution to the equation 2x – 3y = -5
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Section 4.1
Getting y alone We need to learn how to get y alone in an
equation. This will help us identify the slope.1: Get rid of fractions.2: Remove parentheses.3: Combine like terms.4: Get all the y’s on one side and everything else on the other side.5: If there’s a number in front of y, divide both sides by it.6: Simplify if necessary.
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Getting Y Alone
Example: Solve 3x + 5y = 15
3x - 3x + 5y = -3x + 15 Subtract 3x from each side to get the y-term alone.
5y = -3x + 15 Simplify on each side.
Divide by 5 on both sides.
Simplify.353
515
53
5
5
xy
xy
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Getting Y Alone
Solve 4x + 2(5 - y) = 6 for y.
4x + 10 - 2y = 6 Use the dist. prop. to get rid of parenths.
4x + 10 - 10 - 2y = 6 - 10 Subtract 10 from each side to get y-term alone.
4x - 2y = -4
4x - 4x - 2y = -4x - 4 Subtract 4x from each side to get y-term alone.
-2y = -4x – 4
Divide each side by -2 to get y alone.
y = 2x + 2
24
24
2
2
xy
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Section 4.1
Finding Missing Coordinates Given an x or y. Plug into equation to find missing coordinate.
Example: Find the missing coordinate: 2x + 3y = 5 and (2, ?)
2(2) + 3y = 5 Plug in 2 for x.
4 + 3y = 5 Simplify.
3y = 1 Subtract 4 from each side to get y-term alone.
y = 1/3 Divide both sides by 3 to get y alone.
The point is (2, 1/3).
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Section 4.2: Graphing a Linear Equation
Steps for Graphing a Linear Equation1. Determine three ordered pairs that are
solutions to the equation.2. Plot the points.3. Draw a straight line through the points.
Example: Let’s graph the equation 2x + y = 6
To determine three points, we get to pick numbers for x and/or y!
We’ll do that on the next slide.
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Finding Points
Graph 2x + y = 6.
x 2x + y = 6 y (x, y)
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Graphing
Plot the points:
(0, 6)
(3, 0)
(1, 4)
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Memory Aids for Lines
HOY Horizontal lines. 0: Zero (0) slope. Y = number will be what the equation looks like.
VUX Vertical lines. Undefined slope. X = number is what the equation will look like.
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Section 4.3: The Slope of a Line
Slope Tells us how the line will slant on the graph.
Formula: m =
Example: Find the slope of a line that passes through the points (2, 3) and
(5, 7).
m =
m =
12
12
xx
yy
2537
34
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Section 4.3
Slope – Intercept Form y = mx + b m is slope. (0, b) is the y-intercept.
Example: What is the slope and y-intercept for y = -5x + 7?
Slope is -5.
(0, 7) is the y-intercept.
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Section 4.3
Parallel Lines Same Slope!
Example: Line A has a slope of 5. What is the slope of every line parallel to Line A?
Since parallel lines have the same slope, the slope must be 5.
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Section 4.3
Perpendicular Lines Opposite, Reciprocal Slopes
Example: Line A has a slope of 5. What is the slope of every line perpendicular to Line A?
Since perpendicular lines have opposite, reciprocal slopes, the slope must be .
51
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