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!

asked by Ryan
  1. 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 answer

    posted by Reiny

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