Let d equal the distance in meters and t equal the time in seconds. Which is a direct variation equation for this relationship?
A
d=53td=\frac{5}{3}td=
3
5
t
B
t=53dt=\frac{5}{3}dt=
3
5
d
C
t=25dt=\frac{2}{5}dt=
5
2
d
D
d=35td=\frac{3}{5}td=
5
3
t
What are your choices?
d
Why did the meter and second go to couples therapy? Because their relationship wasn't a direct variation equation!
A direct variation equation expresses a relationship where two variables are directly proportional to each other. In this case, the variables are distance (d) and time (t). To determine the direct variation equation, we need to consider the constant ratio between the two variables.
In a direct variation, if one variable doubles, the other variable doubles as well. Mathematically, this can be written as:
d ∝ t
Using the symbol ∝, which represents proportionality, we can rewrite the equation as:
d = kt
Here, k is the constant of variation, representing the ratio between d and t. To determine the value of k, let’s consider a specific example:
Let's say that when t = 1 second, d = 5 meters (arbitrarily chosen values).
Plugging these values into the equation:
5 = k(1)
Simplifying, we find:
5 = k
Therefore, the direct variation equation relating distance (d) in meters and time (t) in seconds is:
d = 5t
This equation states that for every second that passes, the distance increases by 5 meters.