find the function rule
x -2 -1 0 1 2
y 9 4 -1 -6 -11
(-2,9) (0, -1)
I chose two points (x,y)
first I will find the slope:
(-1 -9)/(0 - (-2)) = -10/2 = -5
use m = -5 (0, -1) -1 = b
y = -5x -1
Check a couple other points to make sure they work.
x y change in y/change in x which is slope
-2 9
****** -5
-1 4
****** -5
0 -1
****** -5
1 -6
****** -5
2 -11
hmmm, constant slope = -5
y = -5 x + b
9 = -5 (-2) + b
9 = 10 + b
b = -1
so
y = -5 x -1 answer
check at last point
-11 = -5(2) -1
-11 = -10 - 1 yes, good
To find the function rule that relates the values of x and y in the given table, we need to look for a pattern or relationship between the two sets of numbers. One way to approach this is by observing the changes in values between consecutive x and y pairs.
If we examine the differences between the x-values, we see that they are increasing by 1 each time: -2, -1, 0, 1, 2.
Similarly, when we look at the differences between the y-values, we find that they are decreasing by 5 each time: 9, 4, -1, -6, -11.
Based on these observations, we can conclude that the rule for this function is to subtract 5 from the given x-value to obtain the corresponding y-value. In other words, the function rule is y = x - 5.
Let's confirm this rule by applying it to the given x-values:
For x = -2, y = -2 - 5 = -7 (which matches the y-value of 9)
For x = -1, y = -1 - 5 = -6 (which matches the y-value of 4)
For x = 0, y = 0 - 5 = -5 (which matches the y-value of -1)
For x = 1, y = 1 - 5 = -4 (which matches the y-value of -6)
For x = 2, y = 2 - 5 = -3 (which matches the y-value of -11)
All the calculated y-values match the original y-values, confirming that the function rule y = x - 5 is correct.