The Slope of a Line
Example
Find y if the line through (2,y) and (-2,9) has the slope of
 .
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Check: |
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Multiply each side by (-4) |
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| 9 - y = 6 |
Simplify Fraction |
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| - y = - 3 |
Addition property |
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| y = 3 |
Multiplication property |
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The letter P refers to any point (x, y) and is usually subscripted to match the "subscripts" on the x
and y for each point. The line is drawn through the points located at the particular coordinates listed.
| It really doesn't matter which point is P1(x1,
y1) and which point is P2(x2, y2)!
When you draw a line through the points it will either go up (or go down)
as you look at it from left to right. Some are "steeper" than others so we
judge the "slope" by comparing the "vertical change" dy with the
"horizontal change" dx and since builders have always judged the "pitch of
a roof" using the ratio of the "rise" over the "run" math uses the same
idea and call it "slope". |
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If you put the x-value and y-value for each of your points on a table- you know
that “pairing“ two arithmetic sequences will give you a straight line and you know that these points
are on a line. Put these thoughts together and see that you can find the difference in the two
x-values (dx) and the difference in the two y-values (dy) and use these to find the next two
numbers in each sequence just as you did in the first part of the notes for the chapter. Also, the “dxâ€
and the “dy†you found are values you can put in your “ratio†for the “rise (dy) over run (dx)†thus,
the slope.
Example 1.
The rise (dy) is 2 and the run (dx) is 3
 the roof goes up 2 feet for every
3 feet “over†on the floor. Thus, the slope: m = dy/dx = 2/3
Example 2.
The rise (dy) is 3 and the run (dx) is 2
the roof goes up 3 feet for every
2 feet “over†on the floor. Thus, the slope: m = dy/dx = 3/2
Look carefully and see that the line in #2 is steeper than the line in
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