What does this mean? Do I graph this or what?
Find the variation constant and an equation of variation where y varies directly as x and y=12 when x=2
The variation constant =?
The equation of variation is y=?
the statement "y varies directly as x" can be written as
y = kx, where k is the variation constant
we are given y=12 when x=2, so
12 = 2k
k=6,
so the variation constant is 6 and the equation is
y = 6x
Thank you Reiny
Thanks!
To find the variation constant and the equation of variation, you can follow these steps:
Step 1: Understand the problem
The problem states that y varies directly as x, which means that when x increases, y also increases proportionally. In this case, you are given the specific values of y and x.
Step 2: Recall the formula for direct variation
The formula for direct variation is y = kx, where k represents the variation constant.
Step 3: Use the given values to find the variation constant
You are given that y is equal to 12 when x is equal to 2. By plugging these values into the formula for direct variation, you get:
12 = k * 2
To find k, isolate it by dividing both sides of the equation by 2:
12/2 = k * 2/2
6 = k
Therefore, the variation constant (k) is 6.
Step 4: Write the equation of variation
Now that you have the value of k, you can write the equation of variation using the formula y = kx:
y = 6x
Therefore, the equation of variation where y varies directly as x is y = 6x.
To summarize, the variation constant is 6, and the equation of variation is y = 6x.