suppose y varies directly with x and y=1 when x= -3. what is the constant of variation? what is x when y=4?
K = y/x = 1/-3 = -1/3.
y/x = -1/3
4/x = -1/3
-x = 12
X = -12.
To find the constant of variation in a direct variation equation y = kx, we can use the given information.
Given: y varies directly with x, and y = 1 when x = -3.
Step 1: Plug the given values into the direct variation equation to find the constant of variation (k).
1 = k * (-3)
Step 2: Solve the equation for k.
k = 1 / (-3)
k = -1/3
Therefore, the constant of variation (k) is -1/3.
To find the value of x when y = 4, we can use the direct variation equation y = kx.
Given: y varies directly with x, and k = -1/3.
Step 1: Plug the given values into the direct variation equation to find x.
4 = (-1/3) * x
Step 2: Solve the equation for x.
Multiply both sides by -3 to get rid of the fraction:
-12 = x
Therefore, when y = 4, x = -12.
To find the constant of variation, we can use the given information that "y varies directly with x" and that y=1 when x=-3.
When two variables vary directly, it means that they have a constant ratio. Mathematically, this relationship can be expressed as:
y = kx
Where "k" is the constant of variation.
Given that y=1 when x=-3, we can substitute these values into the equation to solve for k:
1 = k*(-3)
Simplifying the equation, we have:
k = -1/3
Therefore, the constant of variation is -1/3.
Now, let's find x when y=4 using the constant of variation:
4 = (-1/3) * x
To isolate x, we can multiply both sides of the equation by (-3):
-12 = x
Hence, when y=4, x is equal to -12.