Suppose that Y varies directly with X, and Y=16 when X=10.
(a) Write a direct equation that relates X and Y
Equation:
(b) Find Y when X=15
Y=
y = 16/10 x
(a) The direct equation that relates X and Y is Y = kX, where k is the constant of variation.
(b) To find Y when X = 15, we can use the given information that Y = 16 when X = 10.
By substituting these values into the direct equation, we have:
16 = k * 10
To solve for k, divide both sides by 10:
k = 16/10
k = 1.6
Now, we can substitute the value of k into the direct equation to find Y:
Y = 1.6 * 15
Y = 24
(a) The direct equation that relates X and Y can be written as:
Y = kX
where k is the constant of proportionality.
(b) To find Y when X = 15, we need to substitute the given values into the equation. First, we need to find the value of k. We can do this by using the given data: Y = 16 when X = 10. Substituting these values into the equation, we get:
16 = k(10)
To solve for k, divide both sides of the equation by 10:
16/10 = k
k = 1.6
Now that we know the value of k, we can substitute it back into the original equation to find Y when X = 15:
Y = 1.6(15)
Y = 24
To write a direct equation that relates X and Y, we need to determine the constant of variation, which represents how much Y changes for every unit change in X.
Given that Y varies directly with X, we can write the equation as Y = kX, where k is the constant of variation.
To determine the value of k, we can use the given information Y = 16 when X = 10. Substituting these values into the equation: 16 = k * 10.
To solve for k, divide both sides of the equation by 10:
k = 16 / 10 = 1.6.
Therefore, the equation that relates X and Y is Y = 1.6X.
(b) To find Y when X = 15, substitute X = 15 into the equation Y = 1.6X:
Y = 1.6 * 15 = 24.
Therefore, when X = 15, Y = 24.