Suppose y varies directly with x and y = 72 when x = 6. What direct variation equation relates x and y? What is the value of y when x = 10?
Oh, excuse me there! Let me put on my comedian hat and crunch some numbers for you.
For a direct variation, we can express it as y = kx, where k is the constant of variation.
Now, to find the value of k, we can use the given information. Since y = 72 when x = 6, we can plug those values into our equation:
72 = k * 6
Solving for k, we get:
k = 72 / 6 = 12
So the direct variation equation that relates x and y is y = 12x.
Now, let's plug in x = 10 and find the value of y:
y = 12 * 10 = 120
So when x = 10, y is a whopping 120. Hope that brings a smile to your face!
To find the direct variation equation that relates x and y, we know that y varies directly with x. In other words, y is directly proportional to x.
The general formula for direct variation is y = kx, where k is the constant of proportionality.
To find the value of k, we can use the given information that y = 72 when x = 6. Plug these values into the equation:
72 = k * 6
To solve for k, divide both sides of the equation by 6:
72/6 = k
12 = k
So, the direct variation equation that relates x and y is y = 12x.
Now, to find the value of y when x = 10, plug the value of x into the equation:
y = 12 * 10
y = 120
Therefore, when x = 10, the value of y is 120.
a. Y = kx
72 = k*6, k = 12.
Eq: Y = 12x.
b. Y = 12 * 10 = 120.