In a table, how do you tell if y varies directly with x and write an equation if it does?
if each value of y is the same multiple of x, it varies directly. If you can multiply each value of x by some number, k, and get the corresponding value of y, then k is the constant of variation, and
y = kx
I got it already but thanks anyways Steve :)
To determine if y varies directly with x in a table, you need to check if there is a constant ratio of y to x for each row of data.
1. Look at the y values for each row and check if they are proportional to the x values.
- If the ratio of y to x is the same for all rows, then y varies directly with x.
- If the ratio of y to x is different for each row, then y does not vary directly with x.
2. To write the equation for y varying directly with x, use the form:
y = kx
- "k" represents the constant of variation. It is the ratio of y to x.
- Substitute the value of k obtained from the table into the equation.
Note: When determining if y varies directly with x, it is essential to have multiple data points in the table to establish a pattern.
To determine if y varies directly with x in a table, you need to check if the ratio of y-values to x-values remains constant throughout the table. Here's what you need to do:
1. Look closely at the values in the table for x and y.
2. Calculate the ratio of each pair of y-values and x-values. In other words, divide y by x for each row in the table.
3. If the ratios are all the same, then y varies directly with x. This means that for every increase or decrease in x, there is a proportional change in y.
4. To write the equation for the direct variation, you can use the form y = kx, where k is the constant of variation. The value of k can be obtained by taking any pair of x and y values and dividing y by x.
Let's work through an example:
Suppose we have the following table:
|x | y |
|--|--|
|1 | 5 |
|2 | 10|
|3 | 15|
1. Calculate the ratios of y and x for each row:
- For the first row: 5/1 = 5
- For the second row: 10/2 = 5
- For the third row: 15/3 = 5
2. Since the ratios are all the same (5), we can conclude that y varies directly with x.
3. Now, we'll write the equation for the direct variation: y = kx. To find the value of k, we can take any pair of x and y values. Let's choose the first row: 5 = k * 1. Therefore, k = 5.
4. The equation for the direct variation is y = 5x.
By following these steps, you can determine if y varies directly with x and write the corresponding equation.