Find the function rule
X= -2,-1,0,1,2
Y= 9,4,-1,-6,-11
How do you do it at least, you don't have to give the answer I just need help understanding it
as x goes up by 1, y goes down by 5
so, the slope is -5, and
y = -5x+b
when x=0, y=-1, so
y = -5x-1
To find the function rule, we need to determine the relationship between the values of X and Y.
From the given values, we can see that as X increases by 1, Y decreases by 5. This suggests that there is a constant rate of change between X and Y.
To find the slope, we can choose any two points from the data given and use the formula:
Slope = (change in Y) / (change in X)
Let's choose the points (-2, 9) and (0, -1):
Slope = (-1 - 9) / (0 - (-2))
= -10 / 2
= -5
So, the slope between X and Y is -5.
Next, we need to find the y-intercept of the function. We can choose any point from the given data and substitute it into the equation:
Using the point (0, -1):
Y = mx + b, where m is the slope and b is the y-intercept.
-1 = (-5)(0) + b
-1 = 0 + b
b = -1
Therefore, the y-intercept of the function is -1.
Now we can write the function rule:
Y = -5X - 1
So, the function rule for the given data is Y = -5X - 1.