I need to find the equation for these function tables (ex. y=2x). Is there a general formula for finding the equation, or do I have to guess each time?
1. (4,3) (6,13) (8,23)
2. (5,22) (6,15) (7,8)
3. (4, 90) (6,82) (8,72)
To find the equation for a function table, you need to observe the pattern in the given data points. In this case, we have three different sets of data points, so let's analyze each one separately:
1. (4,3) (6,13) (8,23)
Looking at the x-values (4, 6, 8), we can see that they are increasing by 2 each time. Looking at the corresponding y-values (3, 13, 23), we can notice that they are increasing by 10 each time. This means that for every increase of 2 in x, the y-value increases by 10. Therefore, the equation for this table is y = 10x - 17.
2. (5,22) (6,15) (7,8)
In this case, the x-values (5, 6, 7) are increasing by 1 each time. However, the y-values (22, 15, 8) are decreasing by 7 each time. So, for every increase of 1 in x, the y-value decreases by 7. Therefore, the equation for this table is y = -7x + 57.
3. (4, 90) (6,82) (8,72)
For this set, the x-values (4, 6, 8) are increasing by 2, while the y-values (90, 82, 72) are decreasing by 8. So, for every increase of 2 in x, the y-value decreases by 8. Therefore, the equation for this table is y = -4x + 106.
By carefully analyzing the pattern in the data points, you can find the equation for each function table. Note that there is no general formula to find the equation for any function table, as it depends on the specific pattern present in the data points.