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  1. Suppose y varies directly with x, and y = 14 when x = –4. What is the value of y when x = –6?

a.) –21

b.) 10

c.) 18

d.) 21

  1. Suppose y varies directly with x, and y = 25 when x = 140. What is the value of x when y = 36?

a.)140

b.)165

c.)201.6

d.)176

  1. The point (12, 9) is included in a direct variation. What is the constant of variation?

a.)one half

b.)three fourths

c.)1

d.)2

Verified Answer :

  1. - D, 21
    2 - C, 201.6
    3 - B, 3/4

    If you're taking lesson 2: direct variation, Unit 6: Linear Functions, then there should be 2 other questions.
    4 - A, 1/4
    5 - B, 200 

    Hope this helps! :)
IsrarAwan

The correct answers are:

(1) Option (D) 21

(2) Option (C) 201.6

(3) Option (B) three fourths

Explanations:

(1) In order to find the value of y at x=-6, we will first use the line equation (with y-intercept = 0) to find the slope:

y=mx

@ (-4, 14)

14 = m(-4)

m = -14/4 = -3.5

Now that we have the slope value, we can now find the value at x = -6 by using this slope value (-3.5):

y = mx

@ (-6, ?)

y = (-3.5)(-6)

y = 21

Hence the correct answer is: 21 (Option D)

(2) In order to find the value of x at y=36, we will first use the line equation (with y-intercept = 0) to find the slope:

y=mx

@ (140, 25)

25 = m(140)

m = \(\frac{5}{28}\)

Now that we have the slope value, we can now find the value at y = 36 by using this slope value (\(\frac{5}{28}\)):

y = mx

@ (?, 36)

36 = (\(\frac{5}{28}\))(x)

x = 201.6

Hence the correct answer is: 201.6 (Option C)

(3) To find the constant of variation, we use the following formula:

\(k = \frac{y}{x}\) -- (1)

Where k = Constant of variation

y = 9

x = 12

Plug in the values of x and y in equation (1):

(1) => \(k = \frac{9}{12}\)

\(k = \frac{3}{4}\) (Option B)

Hence the correct answer is three fourths (Option B).

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