Research Paper On Slope

Section 2.4
More on Slope

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Section 2.4 More on Slope

Parallel and Perpendicular Lines

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Section 2.4 More on Slope

y = 2x+7

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Section 2.4 More on Slope

Parallel Lines

Find a line parallel to - x  6 y  8 and passing through (-2,3).
-x  6 y  8
Solve for y
6y  x  8
1
4
1
y  x
Use the slope
6
3
6
1 y  3  ( x  2)
Substitute into the point-slope form
6
1
1
y 3  x 
6
3
1
1 y  x 3
6
3
1
10 y  x
6
3
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Section 2.4 More on Slope

Example
Write the equation in slope-intercept form for a line that is parallel to 3x - 4y = 12 and passing through
(5,2).

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Section 2.4 More on Slope

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Section 2.4 More on Slope

Perpendicular Lines
Find a line perpendicular to - x  6 y  8 and passing through (-2, 3).
-x  6 y  8
Solve for y
6y
What does this slope represent? 











x


















x years after 1997







The percent of US adult cigarette smokers is decreasing by .52 percent each year. The change is consistent each year.
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Section 2.4 More on Slope

The Average Rate of Change of a Function

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Section 2.4 More on Slope

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Section 2.4 More on Slope

The Average Rate of Change of a
Function
If the graph of a function is not a straight line, the average rate of change between any two points is the slope of the line containing the two points. This line is called a secant line. y 

( x2 , f ( x2 ))





f ( x2 )  f ( x1 ) x2  x1



Secant line





( x1, f ( x1))





 x 






















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Section 2.4 More on Slope

Find the equation of the line that is parallel to 3x - 5 y  8 and passes through the point (4,-5).
(a)

(b)

(c)

(d)

3
7
y  x
5
5
3
y  x9
5
5
7
y - x
3
5
3
37 y  x
5
5
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Section 2.4 More on Slope

Find the equation of the line that is perpendicular to 8 x - 3 y  6 and passes through (-1,3).
(a)

(b)

(c)

(d)

3 y  x6
8
8
21
y - x
3
8
3
21 y - x
8
8
8
y  - x6
3
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Section 2.4 More on