Determine whether y varies directly with x. If so, find the constant of variation k.
3y = -7× - 18
(1 point
• yes; 3
• yes; -7
• no
7
O yes; 3
To determine if y varies directly with x, we can rewrite the equation in the form y = kx, where k is the constant of variation.
Starting with the given equation:
3y = -7x - 18
Dividing both sides of the equation by 3:
y = (-7/3)x - 6
We can see that the equation is not in the form y = kx, so y does not vary directly with x.
So the correct answer is: no
Multiple Choice
Determine whether y varies directly with x. If so, find the constant of variation k and write the equation.
X
6
18
54
162
y
24
72
216
648
(1 point)
• yes; k =4; y = 4x
• ves: k = 3; y = 3x
• yes: k = 6; y = 6x
- no
To determine if y varies directly with x, we can check if the ratio of y to x is constant. Let's calculate the ratio for each pair of values:
For the pair (6, 24):
Ratio = y / x = 24 / 6 = 4
For the pair (18, 72):
Ratio = y / x = 72 / 18 = 4
For the pair (54, 216):
Ratio = y / x = 216 / 54 = 4
For the pair (162, 648):
Ratio = y / x = 648 / 162 = 4
Since the ratio of y to x is constant for all pairs of values, we can conclude that y varies directly with x. The constant of variation, k, is equal to this constant ratio. In this case, k = 4.
Therefore, the correct answer is: yes; k = 4; y = 4x
Find the value of y for a given value of x, if y varies directly with x.
If y = 2.52 when x = 8.4, what is y when x = 2.7?
(1 point)
• 9
- -9
- 0.81
• -0.81
If y varies directly with x, we can write the equation as y = kx, where k is the constant of variation.
To find the value of y when x = 2.7, we need to determine the value of k first. We can use the given values of y and x to find k:
y = 2.52 and x = 8.4
Plugging these values into the equation, we have:
2.52 = k * 8.4
Dividing both sides of the equation by 8.4, we get:
k = 2.52 / 8.4 = 0.3
Now that we have the value of k, we can find y when x = 2.7:
y = 0.3 * 2.7 = 0.81
Therefore, the correct answer is: 0.81
A broken faucet leaks one gallon of water every 1 months. The amount of months that pass, m, varies directly with the amount of gallons that are leaked, g. Find the equation that models this direct variation. How many months will it take for the faucet to leak 7
gallons of water?
(1 point)
3
O m=.
78, 95 months
3
O m =.
§8.91 months
O m==
8.54 months
- 1
O m=.
58.5
• months
To find the equation that models the direct variation between the number of months that pass, m, and the amount of gallons that are leaked, g, we can use the formula y = kx.
In this case, we have m as y and g as x. We're given that one gallon of water leaks every 1 month. Therefore, the constant of variation, k, is simply 1.
So the equation that models this direct variation is:
m = 1 * g
m = g
To find out how many months it will take for the faucet to leak 7 gallons of water, we plug in g = 7 into the equation:
m = 7
Therefore, it will take 7 months for the faucet to leak 7 gallons of water.
The correct answer is: 7.
A broken faucet leaks one gallon of water every 1 1/3 months. The amount of months that pass, m, varies directly with the amount of gallons that are leaked, g. Find the equation that models this direct variation. How many months will it take for the faucet to leak 7
gallons of water?
1. m = 3/4g, 9 1/3 months
2. m = 4/3g, 9 1/3 months
3. m = 3/4g, 5 1/4 months
4. m = 4/3g, 5 1/4 months
To find the equation that models the direct variation between the number of months that pass, m, and the amount of gallons that are leaked, g, we can use the formula y = kx.
In this case, we have m as y and g as x. We're given that one gallon of water leaks every 1 1/3 months. To convert this to a single fraction, we can rewrite it as 4/3 months per gallon.
Therefore, the constant of variation, k, is 4/3.
So the equation that models this direct variation is:
m = (4/3)g
Now, to find out how many months it will take for the faucet to leak 7 gallons of water, we plug in g = 7 into the equation:
m = (4/3) * 7 = 28/3 = 9 1/3 months
Therefore, the correct answer is:
m = (4/3)g, 9 1/3 months
Option 2 is the correct answer.
What is the graph of the direct variation equation?
y = 5/2x