Determine if two variables are directly proportional. if so, write the equation of variation.
Length measured in centimeters (c) and length measured in inches (i).
no ideas at all, even after the ones we have done for you already?
To determine if two variables are directly proportional, we need to check if their ratio remains constant as one variable changes while the other remains constant.
In this case, we have length measured in centimeters (c) and length measured in inches (i). To check if they are directly proportional, we can divide the length in inches by the length in centimeters for different values.
For example, let's consider two different measurements:
- Length in centimeters (c₁) = 10 cm
- Length in inches (i₁) = 3.94 inches
We calculate the ratio by dividing the length in inches by the length in centimeters:
- Ratio (r₁) = i₁ / c₁ = 3.94 / 10 = 0.394
Now, let's consider another set of measurements:
- Length in centimeters (c₂) = 20 cm
- Length in inches (i₂) = 7.87 inches
We calculate the ratio again:
- Ratio (r₂) = i₂ / c₂ = 7.87 / 20 = 0.394
If the ratio remains the same for different values of the variables, then the two variables are directly proportional.
In this case, we can see that the ratio (r₁ = r₂ = 0.394) remains constant. Therefore, we conclude that length measured in centimeters (c) and length measured in inches (i) are directly proportional.
To write the equation of variation, we can use the general form of a direct variation equation: y = kx, where y represents the dependent variable, x represents the independent variable, and k represents the constant of variation.
In this case, we can let c represent the dependent variable (length in centimeters) and i represent the independent variable (length in inches). The equation of variation would be:
c = ki
To find the value of k, we can substitute the values from any of the ratios calculated earlier:
0.394 = k * 1
Therefore, the equation of variation for length measured in centimeters (c) and length measured in inches (i) is:
c = 0.394i