B. Determine If The Tables And Graphs Below Express A Direct Variation Be…

B. Determine if the tables and graphs below express a direct variation between the va

If they do, find the constant of variation and an equation that defines the relation.

1.

2

2.

6.

3.

5.

X

y

X

X

y

X

X

y

X

y

y

y

1

-3

7

3

2

6

7

-21

6 -9

-15 10 -20 25

-3 2

5

3

2

16

20

12 15

3

-9

8

9

4

– 12

4

3

-28

-12

5

4

24 28

32

18 21 24

10

12

11 13

Answer:

To determine if the tables and graphs express a direct variation, we need to check if the ratios of y to x are constant. Let’s calculate these ratios for each set of values:

1. \( \frac{-3}{1} = -3 \)

2. \( \frac{6}{2} = 3 \)

3. \( \frac{-21}{7} = -3 \)

4. \( \frac{-9}{3} = -3 \)

5. \( \frac{10}{2} = 5 \)

6. \( \frac{-15}{-5} = 3 \)

Since the ratios are constant (-3, 3, -3, -3, 5, 3), we can conclude that there is a direct variation.

Now, let’s find the constant of variation (k). It’s the common ratio in the direct variation equation \(y = kx\).

For example, using the first set: \( -3 = k \times 1 \), so \( k = -3 \).

Thus, the equation defining the relation is \(y = -3x\).

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