suppose y varies directly with x, and y=12 when x=-4. find x when y=15.
x=?
since y=kx, y/x=k which is constant. So, you want x such that
15/x = 12/-4
Well, you know what they say, "If y varies directly with x, then x is the what makes y want to dance!" Let's get to the bottom of this!
If y = 12 when x = -4, we can use this information to find the constant of variation. Since y varies directly with x, we can write the equation as y = kx, where k is the constant of variation.
So, substituting the given values, we have 12 = k * (-4). Dividing both sides by -4, we get k = -3.
Now that we have the constant of variation, we can find x when y = 15. Plugging these values into the equation, we have 15 = -3x. Dividing both sides by -3, we find x = -5.
So, x = -5 is the answer! The variable x always knows how to make y groove!
To find x when y = 15, we can use the direct variation equation:
y = kx
First, we need to find the constant of variation (k). We can do this by substituting the given values of y and x:
12 = k(-4)
To solve for k, divide both sides of the equation by -4:
k = 12 / -4
k = -3
Now that we have the value of k, we can substitute it into the equation and solve for x when y = 15:
15 = -3x
Divide both sides of the equation by -3:
x = 15 / -3
x = -5
Therefore, when y = 15, x is equal to -5.
To find the value of x when y=15, we can use the concept of direct variation. When two variables vary directly with each other, it means that they are related by a constant ratio.
In this case, we are told that y varies directly with x. We can express this relationship using the equation y = kx, where k is the constant of variation.
To find the value of k, we can use the given information. We are given that y = 12 when x = -4. Substituting these values into the equation, we have:
12 = k(-4)
To solve for k, divide both sides of the equation by -4:
k = 12 / -4
k = -3
Now we know the constant of variation is -3. We can use this constant to find the value of x when y = 15.
Using the equation y = kx, and substituting the known values, we have:
15 = -3x
To solve for x, divide both sides of the equation by -3:
x = 15 / -3
x = -5
Therefore, when y = 15, x is equal to -5.