The instructions to my book work says for the data in each table, tell whether y varies directly with x. If it does write an equation fo rthe direct variations. Well how do you do that exactly.
Thanks you for your help..
Please help me.
To determine whether y varies directly with x, you need to compare the values of y to the corresponding values of x. If there is a consistent ratio between the values of y and x, then y varies directly with x. Here's how you can determine this and write an equation for the direct variation:
1. Start by examining the values in the table. Identify the column that represents the variable x and the column that represents the variable y.
2. Calculate the ratios of the corresponding y and x values for each row in the table. To do this, divide the value of y by the value of x for each row.
3. Compare the ratios you calculated. If the ratios are consistent (i.e., they are always the same), then y varies directly with x. If not, then y does not vary directly with x.
4. If y varies directly with x, you can write an equation for the direct variation. The equation will be in the form y = kx, where k is the constant of variation. You can determine the value of k by taking any row in the table and dividing the value of y by the value of x for that row. The resulting quotient will be the value of k.
For example, let's say you have the following table:
x | y
---------
2 | 8
4 | 16
6 | 24
Here's how you would determine whether y varies directly with x and find the equation of the direct variation:
1. Identify x as the variable in the first column and y as the variable in the second column.
2. Calculate the ratios:
- For the first row: y/x = 8/2 = 4
- For the second row: y/x = 16/4 = 4
- For the third row: y/x = 24/6 = 4
3. Since the ratios are consistent (4 in each case), y varies directly with x.
4. Write the equation of the direct variation: y = kx. To find the value of k, choose any row and divide y by x. Let's use the first row: 8/2 = 4. Therefore, k = 4. So the equation is y = 4x.
By following these steps, you can determine whether y varies directly with x and write the equation of the direct variation if it does.