Suppose y varies directly with x. If y = 6 when x = -2, find x when y = 15.
a. ⅕
b. 5
c. -5
d. -⅕
y = k x
6 = k (-2)
k = -3
15 = -3 x
x = -15/3
x = -5
To find the value of x when y = 15, we can use the direct variation formula:
y = kx
where k is the constant of variation.
First, let's find the value of k using the given information. We are told that when y = 6, x = -2. We can substitute this into the formula:
6 = k(-2)
Solving for k, we divide both sides of the equation by -2:
k = 6 / -2
k = -3
Now that we have the value of k, we can substitute it and the given value of y into the formula to find x:
15 = -3x
Dividing both sides by -3:
x = 15 / -3
x = -5
Therefore, the value of x when y = 15 is -5, which corresponds to option c.