Step-by-step explanation:
Let's use the two noted points for the calculation of slope:
Point 1: (2,8) and
Point 2: (6,4)
These become our (x1,y1) and (x2,y2).
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We are trying to find a straight line equation of the form y = mx+b, where m is the slope and b is the y-intercept (the value of y when x = 0).
The slope:
m = (y2 - y1)/(x2 - x1)
m = (4 - 8)/(6 - 2)
m = -4/4
m = -1
This gives us y = -1x + b
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Find b by entering either of the two given points. I'll use (6,4):
y = -1x + b
4 = -1(6) + b
b = 10
The equation is now y = -x + 10
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Find the value of y when x = 9:
y = -x + 10
y(9) = -(9) + 10
y(9) = 1
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This graph has a negative trend. Y decreases as x increases. It crosses the y axis at 10 when x is 0, and is only positive when x < 10. See the attached graph. Note that the graph of this line does not intersect many of the points on the original graph. They fall to either side, and are not consistent with a single line equation. The general, negative trend of slope - 1 trend holds true, however, so one might conclude errors may have been made in collecting the data. That is clearly due to your lab partner. [Well, you might try a better explanation]. A craftier person might calculate a standard deviation of error for the line, but that's next semester. It is worthwhile noting that a selection of two points other than the ones chosen above for calculating slope, would result in different equations. We selected the two points used here ((2,8) and (6,4)) because they are clearly noted on the chart.
