Algebra 2 Honors
Hey, we recently started a topic in class that I don't understand well, I just want to post 6 of the problems and ask if they're right or not (some of them I have no idea how to do).
1. If a varies directly as b and b = 18 when a = 27, find a when b = 10.
For this I did 27/18 = a/10 and my answer was a = 15.
2. If y varies inversely as x and y = 3 when x = 9, find y when x = 81.
For this I did 3/81= = y/9 and my answer was y = 1/3.
3. If y varies jointly as x and z, and y = 18 when x = 6 and z = 15, find y when x = 12 and z = 4.
For this I did 18/12*4 = y/6*15 and my answer was y = 33.75.
Direction variation can be expressed in the form of y = kx and inverse variation can be expressed in the form of y = k/x, right?
Last off is the part I didn't understand.
Is the relationship between the variables in set of data a direct variation, inverse variation, or neither? Indicate the constant of variation, if applicable.
a. {(0.5, 1.5), (2, 6), (6, 18)} I said this is direct variation though no idea how to get the constant of variation.
b. {(0.2, 12), (0.6, 4), (1.2, 2)} I said this was inverse variation but yet again no idea how to get the constant of variation.
c. {(1, 2), (2, 1), (3, 0.5)} I said this was neither, and I expect there is no constant of variation?
I do understand this is quite long, for whoever and if someone even does help me with this, thank you!

you did your first 3 questions by using ratios.
This is fine as long as you know where to put the numbers.
since you appear to understand that
direct variation > y = kx
inverse variation > y = k/x
perhaps that is the approach you might take at the beginning.
1. It says direct variation, so a = kb
we are told, a=27, and b = 18, so
27 = 18k
k = 27/18 = 3/2
so we know a = (3/2)b
now if b = 10
a = (3/2)(10) = 15
2. is correct
3. Using the k method:
y = k(xz)
given: x=6, y=18, z=15
18 = k(90) > k = 1/5
so y = (1/5)xz
when x=12, z=4 , then
y = (1/5)(12)(4) = 48/5
Your last part:
recall that for direct variation: y = kx, so k = y/x
now look at the ordered pairs, is
18/6 = 6/2 = 1.5/.5 ??? yes, all 3 are equal to 3, so it is a direct variation
for in inverse we have y = k/x > k = xy
look at your given points
In all cases, xy = 2.4 , so your answer of inverse is correct
for c) points are (1,2), (2,1), (3, .5)
1x2 = 2x1 ≠ 3x.5, so it is not inverse variation
2/1 ≠ 1/2 , no point going further, not direct
so neither is the correct answerposted by Reiny
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