The values of x and y vary directly and one pair of values are given. Write an equation that relates x and y. Simplify completely.
x=0.1, y=0.9
y=?x
y = m x
.9 = m (.1)
m = 9
y = 9 x
If the values of x and y vary directly, it means that they can be related through a proportion. The equation that relates x and y is given by:
y = kx
where k is the constant of variation.
To find the value of k, we can use the given pair of values x=0.1 and y=0.9:
0.9 = k(0.1)
To solve for k, divide both sides of the equation by 0.1:
0.9/0.1 = k
Simplifying this equation gives us:
k = 9
So the equation that relates x and y is:
y = 9x
Therefore, if you want to find y in terms of x, the relationship is y = 9x.
To write an equation that relates two variables, x and y, when they vary directly, we can use the equation:
y = kx
In this equation, k represents the constant of variation.
To find the specific equation for the given pair of values where x = 0.1 and y = 0.9, we can substitute those values into the equation and solve for k.
0.9 = k(0.1)
To solve for k, divide both sides of the equation by 0.1:
0.9 / 0.1 = k
The result is:
k = 9
Now that we have found the value of k, we can rewrite the equation with the specific constant of variation:
y = 9x
Therefore, the equation that relates x and y when they vary directly is:
y = 9x