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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

2. 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

3. 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

Respuesta :

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 = [tex] \frac{5}{28} [/tex]

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

y = mx

@ (?, 36)

36 = ([tex] \frac{5}{28} [/tex])*(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:

[tex] k = \frac{y}{x} [/tex] -- (1)

Where k = Constant of variation

y = 9

x = 12

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

(1) => [tex] k = \frac{9}{12} [/tex]

[tex] k = \frac{3}{4} [/tex] (Option B)

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

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