I need the answers and the work shown steb by step today pls^^
For each direct variation find the constant of variation.Then find the value of y when x= -5
1.y=2 whne x=7
2.y=-2 when x=2
3.y= 17 when x=-4
y varies directly with x.
1.if y=6 when x=2,find x whn y=12
2.if y=7 when x= -3,find y when x= -1
If there is a direct variation, then y is proportional to x. This can be written y = kx. Use the information you are given to determine k.
1. If y = kx and y=2 when x = 7, then
2 = 7k, and
k = 2/7, so
y = (2/7)x
Whe x = -5, y = -10/7
Do the others the same way.
1. If y=6 when x=2, then k=3 and y = 3x.
When x=12, y = ?
Well thanks but in the other questions im guessing that y stays the same so 1. will be equal to 1/2 and 2.-7/1 correct me if im wrong pls but is also suspicious because it says y varies direclty with x idk what that means
1. For each direct variation problem, we need to use the formula y = kx, where k is the constant of variation.
For the first problem, y = 2 when x = 7, we can use this information to find the constant of variation:
2 = k * 7
To solve for k, divide both sides of the equation by 7:
k = 2/7
Now that we have the constant of variation, we can find the value of y when x = -5:
y = (2/7) * (-5)
y = -10/7
Therefore, when x = -5, y = -10/7.
2. For the second problem, y = -2 when x = 2, we can again use the direct variation formula:
-2 = k * 2
Divide both sides by 2 to solve for k:
k = -2/2
k = -1
Now we need to find y when x = -5:
y = (-1) * (-5)
y = 5
Therefore, when x = -5, y = 5.
3. For the third problem, y = 17 when x = -4, use the direct variation formula:
17 = k * (-4)
Divide both sides by -4 to solve for k:
k = 17/(-4)
k = -17/4
Now find y when x = -5:
y = (-17/4) * (-5)
y = 85/4
Therefore, when x = -5, y = 85/4.
Now moving on to the second set of direct variation problems:
1. For the first problem, we know that y = 6 when x = 2. We can find x when y = 12 using the direct variation formula:
6 = k * 2
Solve for k by dividing both sides by 2:
k = 6/2
k = 3
Now find x when y = 12:
12 = 3x
Divide both sides by 3 to solve for x:
x = 12/3
x = 4
Therefore, when y = 12, x = 4.
2. For the second problem, we know that y = 7 when x = -3. We need to find y when x = -1 using the direct variation formula:
7 = k * (-3)
Divide both sides by -3 to solve for k:
k = 7/(-3)
k = -7/3
Now we can find y when x = -1:
y = (-7/3) * (-1)
y = 7/3
Therefore, when x = -1, y = 7/3.
I hope this helps! Let me know if you have any further questions.