Suppose y varies directly with x, and y = 14 when x = –4. What is the value of y when x = –6?
If y varies directly with x, it means that y can be written as y = kx, where k is the constant of variation.
To find the value of k, we can use the given information that y = 14 when x = –4. Plugging these values into the equation, we get:
14 = k(-4)
Dividing both sides of the equation by -4, we get:
14/-4 = k
Simplifying, we have:
-7/2 = k
Now that we have the value of k, we can find the value of y when x = –6 by plugging the values into the equation:
y = kx
y = (-7/2)(-6)
Simplifying, we have:
y = 21
Therefore, when x = –6, y will have a value of 21.