If y varies directly with x and y is 14 when x is 6
What is the constant of variation
What is the direct variation equation
y = k x ... 14 = k * 6 ... k = 7/3
y = 7/3 x
To find the constant of variation in a direct variation relationship, we can use the formula:
k = y / x
where k is the constant of variation, y is the value of y, and x is the corresponding value of x.
Given that y is 14 when x is 6, we can substitute these values into the formula:
k = 14 / 6
Simplifying the right side of the equation:
k = 7 / 3
Therefore, the constant of variation is 7/3.
Now, let's find the direct variation equation. In a direct variation relationship, the equation is in the form:
y = kx
where y is the dependent variable, x is the independent variable, and k is the constant of variation.
Using the value of the constant of variation we found (k = 7/3), we can write the direct variation equation:
y = (7/3)x
So the direct variation equation for this problem is y = (7/3)x.