Given that y varies directly with x, write a direct variation equation that relates x and y.
x=1/3 <---(fraction), y=2
**Provide an explanation as well, please.
y varies directly with x means
y = kx , where k is a constant.
so for the given:
x=1/3, y = 2
2 = (1/3)k
k = 6
equation: y = 6x
Okay thanks![:
To write a direct variation equation, you need to find the constant of variation (k) first. In this case, since "y varies directly with x," it means that y and x are directly proportional to each other. This can be represented by the formula:
y = kx
To find the value of k, you can substitute the given values of x and y into the equation and solve for k. Given that x = 1/3 and y = 2, we can write the equation as:
2 = (1/3)k
Now we can solve for k by isolating it on one side of the equation. Multiplying both sides by 3 will eliminate the fraction:
2 * 3 = (1/3)k * 3
6 = k
Therefore, the direct variation equation that relates x and y is:
y = 6x
This equation tells us that for every 1 unit increase in x, y will increase by 6 units.