6.1 & 6.2 slope & perpendicular and parallel lines
TRANSCRIPT
6.1 & 6.2 Slope of a Line & Parallel and Perpependicular Lines
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Unit 6 ‐ Linear Functions
1. Slope of a Line2. Parallel and Perpendicular Lines3. Expressing Lines (Equations of Lines)4. Midpoint/distance formulas
6.1 & 6.2 Slope of a Line & Parallel and Perpependicular Lines
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6.1 Slope of a LineReview:What is the...1. Domain2. Range3. X‐Intercept4. Y‐Intercept5. Rate of Change?
6.1 & 6.2 Slope of a Line & Parallel and Perpependicular Lines
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When dealing with linear functions, the rate of change is also known as the slope. Again, the slope (just like the rate of change) measures how one quantity changes with respect to another.
The slope can be measured by looking at the rise and the run of the line.
The rise is the vertical distance from one point on the line to another.
The run is the corresponding horizontal distance between the same two points.
riseslope =
run
6.1 & 6.2 Slope of a Line & Parallel and Perpependicular Lines
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Calculating the Slope of a LineA line passes through A(x1, y1) and B(x2, y2).
The slope of line AB
m =
A(x1, y1)
B(x2, y2)
x2 ‐ x1y2 ‐ y1
**we use the letter 'm' for slope
6.1 & 6.2 Slope of a Line & Parallel and Perpependicular Lines
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Example 1. What is the slope of the line?
6.1 & 6.2 Slope of a Line & Parallel and Perpependicular Lines
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Example 2: Determine the slope of the line
6.1 & 6.2 Slope of a Line & Parallel and Perpependicular Lines
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Example 3. Draw a line segment for the slope 7/5 including the point (1, 2)
6.1 & 6.2 Slope of a Line & Parallel and Perpependicular Lines
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Example 4. Draw a line segment for the slope ‐3/8 including the point (3, ‐2)
6.1 & 6.2 Slope of a Line & Parallel and Perpependicular Lines
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6.1 & 6.2 Slope of a Line & Parallel and Perpependicular Lines
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6.1 & 6.2 Slope of a Line & Parallel and Perpependicular Lines
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Interpreting Slopes
There are 4 situations when dealing with slopes (dealt with this slightly in the last unit)
1. Positive Slope2. Negative Slope3. Zero (0) Slope4. Undefined Slope
6.1 & 6.2 Slope of a Line & Parallel and Perpependicular Lines
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Positive Slopes
‐ increasing rate of change‐ y and x must BOTH be positive OR negative‐ Move up to the right OR down to the left
6.1 & 6.2 Slope of a Line & Parallel and Perpependicular Lines
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Negative Slopes
‐ Either y or x must be negative
‐ Move up to the left OR down to the right
6.1 & 6.2 Slope of a Line & Parallel and Perpependicular Lines
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Zero Slopes
‐ Have a rise of 0 (zero); therefore a HORIZONTAL line
6.1 & 6.2 Slope of a Line & Parallel and Perpependicular Lines
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Undefined Slopes
‐ Have a run of 0 (zero); therefore a vertical line
6.1 & 6.2 Slope of a Line & Parallel and Perpependicular Lines
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6.2 Parallel and Perpendicular Lines
6.1 & 6.2 Slope of a Line & Parallel and Perpependicular Lines
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Parallel lines
Given a line with slope m, a line parallel to that line also has a slope m.
6.1 & 6.2 Slope of a Line & Parallel and Perpependicular Lines
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Perpendicular Lines
If a line is perpendicular to another line with a slope of m,
the first line has a slope ‐1/m, m ≠0
6.1 & 6.2 Slope of a Line & Parallel and Perpependicular Lines
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Example
Line A has the equation y = 2x + 1. Find the equation of the line that is parallel and that passes through the point (5, 4).
6.1 & 6.2 Slope of a Line & Parallel and Perpependicular Lines
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Example
Determine the slope of a line that is perpendicular to the line through E(2, 3) and F(-4, -1).
6.1 & 6.2 Slope of a Line & Parallel and Perpependicular Lines
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6.1 & 6.2 Slope of a Line & Parallel and Perpependicular Lines
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6.1 & 6.2 Slope of a Line & Parallel and Perpependicular Lines
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