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Answer:
17. b. y -3 = 2/3(x +6)
18. b. y -720 = 50(x -12)
19. d. y -237,000 = 5000(x -8)
Explanation:
The given equation is the "point-slope" equation for a line. In order to use it, you need to know a point on the line and the slope of the line. You do this math by identifying those numbers in the problem statement, then filling them into the equation.
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17. You are given the point (x1, y1) = (-6, 3) and the slope m = 2/3. Put those in the given form:
y -y1 = m(x -x1)
y -3 = 2/3(x -(-6))
y -3 = 2/3(x +6) . . . . . . matches choice B
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18. The intended relation is one that relate fees to months. That is, x represents months of membership and y represents fees paid. You are given a monthly rate (slope) of $50 per month, and a point (x, y) = (12, 720) -- the fee after 12 months is $720.
Putting those into the form, you have m = 50, x1 = 12, y1 = 720, so ...
y -y1 = m(x -x1)
y -720 = 50(x -12) . . . . . . . matches choice B
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18. The table gives you several points. The x-value being used is the difference between the year number and 2005. The y-value is the profit. The point that shows up in the answer choices is the last one, (x1, y1) = (8, 237000). You have to figure the slope, but the answer choices all show its magnitude is 5000. You can tell it has positive sign because the profit increases over the years. Using this point and slope in the equation form, you get ...
y -y1 = m(x -x1)
y -237000 = 5000(x -8) . . . . . matches choice D
The slope is ...
(difference in profit)/(difference in years) = (237000 -197000)/(2013 -2005)
= 40000/8 = 5000 . . . . with a positive sign