Suppose y varies directly with x, and y=14 when x=-4. What is the value of y when x=-6?
A. -21
B. 10
C. 18
D. 21
y = kx. In other words,
y/x = k, a constant. So, you want y such that
y/-6 = 14/-4
To find the value of y when x=-6, we can use the concept of direct variation. When two variables, y and x, vary directly, it means that their ratio remains constant.
In this case, we are given that y varies directly with x. We can represent this relationship with the equation y = kx, where k is the constant of variation.
To find the value of k, we can substitute the given values of y and x into the equation. We are given that when x = -4, y = 14. So we have:
14 = k(-4)
Solving for k, we divide both sides of the equation by -4:
k = 14 / -4
k = -3.5
Now that we have the value of k, we can substitute it back into the equation to find the value of y when x = -6:
y = (-3.5)(-6)
y = 21
Therefore, the value of y when x = -6 is 21.
So the answer is:
D. 21