determine whether y varies directly with x, if so, find the constant of variation k and write the equation.
To determine whether y varies directly with x, we check if the ratio of y to x remains constant. In other words, if y = kx, where k is the constant of variation.
If the ratio of y to x is constant for different values of x, then y varies directly with x.
To find the constant of variation k, we divide any y-value by the corresponding x-value and check if the ratio remains constant.
If the ratio remains constant, we can write the equation as y = kx, where k is the constant of variation.
If the ratio does not remain constant for different values of x, then y does not vary directly with x.
Without specific values for y and x, it is not possible to find the constant of variation k or write the equation.
To determine whether y varies directly with x, we need to check whether the ratio of y to x remains constant. If the ratio is constant, y varies directly with x.
Here are the steps to determine if y varies directly with x and find the constant of variation, k:
1. Identify the given data points, which consist of pairs of x and y values.
2. Calculate the ratio of y to x for each data point. Divide the corresponding y-values by their corresponding x-values.
3. Check if the ratios are the same for all data points. If the ratios are constant, y varies directly with x.
4. If the ratios are constant, calculate the constant of variation, k, which is the value of the ratio. Choose any pair of data points and divide the y-value by the x-value to get k.
5. Write the equation of the direct variation. The equation will be in the form y = kx, where k is the constant of variation found in step 4.
Note: If the ratios are not constant for all data points, then y does not vary directly with x.