if y varies directly as x find the direct variation equation for the situation:
y=20 and x=16
if y varies directly as x
becomes
y = kx, where k is a constant
so if y=20 and x=16
20 = 16k
k=5/4
therefore y = (5/4)x
most of these question are that simple.
To find the direct variation equation, we need to determine the constant of variation, which is the ratio between the variables.
In this case, we are given that y varies directly as x. The direct variation equation 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 from the problem. We have the values y = 20 and x = 16. Substituting these values into the equation:
20 = k(16)
To find k, we divide both sides of the equation by 16:
20/16 = k
Simplifying the fraction:
5/4 = k
So, the constant of variation is 5/4. Now, we can rewrite the direct variation equation with the determined constant:
y = (5/4)x
Therefore, the direct variation equation for the given situation is y = (5/4)x.