1. For the data table, does y vary directly with x? If it does, write equation for the direct variation.

x|y 10|15 16|24 20|30
A. Yes; y=1.5x
B. Yes; y=2x **
C. Yes; y=x+5
D. No there is no direct variation.

2. For the data table, does y vary directly with x? If it does, write equation for the direct variation.
x|y 32|24 16|8 8|6
A. Yes; y=0.5x
B. Yes; y=2x
C. Yes; y=1.5x
D. No there is no direct variation. **

Thank you!

#1, yes it is, since 15/10 = 24/16 = 30/20 = 3/2 or 1.5

you had the wrong equation

#2 your are correct

#1 y=2x? I think not.

Does 15 = 2*10 ?

#2 correct

Sorry, I was looking at 24 mainly & got x2 for #1. Thank you!!

Does anyone have the answers from #1 to #24, "6.10.1 - Test: Linear Functions Unit Test"? Thanks!

To determine if y varies directly with x, we need to check if the ratio of y to x remains constant throughout the data table.

For the first data table:
x|y
10|15
16|24
20|30

To check if y varies directly with x, we divide each y-value by the corresponding x-value:

15/10 = 1.5
24/16 = 1.5
30/20 = 1.5

Since the ratio of y to x is constant at 1.5, we can conclude that y varies directly with x.

To find the equation for direct variation, we can use the form y = kx, where k is the constant of variation. To find k, we can choose any x and y value from the data table. Let's use the first pair (10, 15):

15 = k * 10

Solving for k, we get:

k = 15/10 = 1.5

Therefore, the equation for direct variation is y = 1.5x.

For the second data table:
x|y
32|24
16|8
8|6

To check if y varies directly with x, we divide each y-value by the corresponding x-value:

24/32 = 0.75
8/16 = 0.5
6/8 = 0.75

Since the ratio of y to x is not constant, y does not vary directly with x. Therefore, the correct answer is D. No, there is no direct variation.