Hello, Karim,
As in another answer I just posted in response to your questions, I'll give an explanation and a few exampes you ncan use un answering the remaining questions.
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-Find the slope of the line through (3,7) and (-1,4)
The slopeof aline can be though of as the amount a line goes up or down as x increases from left to right. Remember this as "Slope is the Rise over the Run of a straight line." Slope = Rise/Run.
The slope through (3,7) and (-1,4) : I'll first reorder these points so that the lower x value is on the left:
(-1,4) (3,7)
I only do this to make it easier for me to remember which number I subtract from the other,
The Run is (3 -(-1)), or 4 (the distance between the two x points is 4.)
The Rise is (7-4), or 3. The value of y increase by three when x increase by 4. The Rise/Run is therefore 3/4, which is the slope of the line.
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-Find the slope of the line through (-3,2) and (6,2)
Rise/Run = (2-2)/(6-(-3)) or 0/9 = 0. A flat line! No matter what you do to x, y is the same.
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-What is the slope of a vertical line (slope dude)
The slope of a vertical line is 0. x is only one point - it does not change.
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-In 1996 there were 171 area codes in the United States. In 2007, there were 215. Find the rate of change (in lowest terms) from 1996 to 2007.
Rise/Run = (215-171)/(2007-1996) 4 codes/year
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-What is the 12th term in the sequence you wrote above: 12, 15, 18, 21 (hint: use the formula you wrote before)
Add 4 every year.
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-Suppose y varies directly as x and y = 26 when x=8. Find x when y = 65
y = (26/8)x
65 = (13/4)x
x= (65(*4/13)
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I hope this helps,
Bob
