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Find the function rule.
[x| -2| -1| 0| 1| 2]
[y| 9| 4| -1| -6| -11]
PLEASE HELP!!!
note that as x grows by 1, y goes down by 5. So, the slope is -5, and your first guess is
y = -5x
But, it has to be adjusted, since y(0) is not 0...
Wait don't understand can you explain to be better.
oobleck can you give the answers.
To find the function rule relating the variables x and y, we need to determine how the values of x are related to the corresponding values of y.
Looking at the given values, we notice that the y-values are decreasing by 5 each time the x-values increase by 1. This suggests that the function may be linear with a slope of -5.
To confirm this, we can calculate the difference in y-values for each successive pair of x-values. The differences between consecutive y-values are as follows:
-2 to -1: 4 - 9 = -5
-1 to 0: -1 - 4 = -5
0 to 1: -6 - (-1) = -5
1 to 2: -11 - (-6) = -5
We can observe that the differences remain constant at -5. Therefore, we can conclude that the function rule is a linear one with a slope of -5.
To find the y-intercept, we can use any of the given points. Let's use the point (0, -1).
We can use the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept. Substituting the values, we have:
-1 = (-5)(0) + b
-1 = 0 + b
b = -1
Therefore, the function rule relating x and y is:
y = -5x - 1
Read about the slope-intercept form of a line
If y changes by a constant amount as x changes, then that gives you teh slope (m) of the line. Then the equation is
y = mx+b
For this relation, m = -5
Now you just have to find b, the y-intercept. Set x=0 and find y.
If this makes no sense, you clearly have not paid attention in class, nor studied your text.