How do I find the variation constant and an equation of variation where y varies directly as x and y =70 when x=7
http://www.purplemath.com/modules/variatn.htm
See the site above.
I would do
y=kx
y=70
x=7
Therefore, k = 70/7=10 and
the equation is y=10x
y=kx looks like k is y/x
To find the variation constant and the equation of variation, you can use the formula for direct variation:
y = kx
where y is the dependent variable, x is the independent variable, and k is the variation constant.
In this case, you are given that y = 70 when x = 7. To find the variation constant, substitute these values into the equation:
70 = k * 7
Now, solve for k by dividing both sides of the equation by 7:
k = 70 / 7
k = 10
Therefore, the variation constant is 10.
Now that we have the variation constant, we can write the equation of variation:
y = kx
Substituting the value of k, the equation becomes:
y = 10x
Thus, the equation of variation is y = 10x, where y varies directly as x.
To find the variation constant and the equation of variation where y varies directly as x, you can follow these steps:
Step 1: Write down the given information:
y = 70 when x = 7
Step 2: Use the given information to find the variation constant:
Since y varies directly as x, we can set up the equation:
y = kx, where k is the variation constant.
Substitute the given values into this equation:
70 = k * 7
Step 3: Solve for the variation constant:
Divide both sides of the equation by 7:
70 / 7 = k
10 = k
So, the variation constant is k = 10.
Step 4: Write the equation of the variation:
Now that you have the variation constant, you can write the equation of variation as:
y = kx
Substituting the value of k into the equation, we get:
y = 10x
Therefore, the equation of variation where y varies directly as x is y = 10x.