Slopes and Equations of Lines
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Transcript of Slopes and Equations of Lines
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Slopes and Equations of Lines
Lesson 1.1
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The Plot Thickens
We plot ordered pairs (x-coord, y-coord)
Where would we plot (4, -2)?
• (2, 1)
•(-1, -2)
• (-5, 1)
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Line 'em Up
A line is a collection of points• When the x-coordinate is zero it intercepts the
y-axis
• When the y-coordinate is zero, it intercepts the x-axis
x-intercept
y-intercept
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Slope of a Line
Represents the "steepness" of a line• Measured by the change in the y-value divided
by the change in the x-value1 2
1 2
y yyx x x
•(-3, 2)
(3, 0)
2 0 2 13 3 6 3
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Equations of a Line
Slope-Intercept Form
Point-Slope Form
y m x b
1 1y y m x x
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Horizontal, Vertical Lines
Horizontal linesy = 12
• Note: slope is 0
Vertical linesx = 7
• Note: slope is infinite, or "no slope"
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Graphing Lines on the TI Calculator
We wish to graph the equation
Go to the Y= screen – use ♦W or ♦F1Enter the function on the entry line
It appears in thelist
3 4y x
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Graphing Lines on the TI Calculator
Now specify the standard zoom F2 and 6
Function will graph on axes
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Parallel and Perpendicular Lines
Parallel lines have the same slope
Perpendicular lines haveslopes that are negativereciprocals
Graph these to verify, use Zoom-Square
2 732 53
y x
y x
3 22
y x
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Try It OutFind the equation of a line through (2, -5) and parallel to y = 2x + 4
Find the equation of a line with x-intercept of -2/3 and perpendicular to 2x – 3y = 5
A business has sales of $27,000 in its 2nd year, $63,000 in 5th year. Let y be the sales for the xth year. Assume the data can be approximated by a st. line. Determine an equation for the sales• Use your answer to find out how many hears until
sales surpass $100,000
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Assignment
Lesson 1.1Page 15Exercises 1 – 59 EOO, 61, 67, 75