Find the function Rule.
x= -2 -1 0 1 2
y= 9 4 -1 -6 -11
It's hard for me to find the answer. Please help me!
Notice the y values decrease by 5 while the x values increase by 1, so the slope is a constant -5
thus the equation is y = -5x + b
notice that the pair (0,-1) is the y-intercept which is what the b stands for , so ...
y = -5x - 1
check it with some of the other given values, it is correct
y goes down 5 when x goes up 1, so start with
y = -5x
adjust that, since when x=0, y = -1.
Sure, I can help you! Let's take a look at the relationship between x and y.
If we observe the pattern, we can see that for every increase in x by 1, y decreases by 5. So, we can say that the function rule is:
y = -5x - 4
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To find the function rule, we need to determine the relationship between the values of x and y.
Observing the values of x and y, we can see that when x increases by 1, y decreases by 5. This tells us that there is a linear relationship between x and y, with a constant rate of change of -5.
To find the function rule, we can start with the general form of a linear equation: y = mx + b, where m represents the slope (rate of change) and b represents the y-intercept.
Using the given information, we can substitute the values of x and y into the equation to solve for m and b. Let's take one pair of x and y values, for example, x = -2 and y = 9:
9 = (-2)m + b
Now, let's choose another pair of x and y values, such as x = -1 and y = 4:
4 = (-1)m + b
We now have a system of two equations:
9 = (-2)m + b
4 = (-1)m + b
Solving this system of equations for m and b, we can use either substitution or elimination method. Let's use the elimination method.
To eliminate b, we'll subtract the second equation from the first:
(9 - 4) = [(-2)m + b] - [(-1)m + b]
5 = -2m - (-m)
5 = -2m + m
5 = -m
Divide both sides of the equation by -1 to solve for m:
m = -5
Now, substitute the value of m into one of the original equations to solve for b. Let's use the equation 4 = (-1)m + b:
4 = (-1)(-5) + b
4 = 5 + b
4 - 5 = b
-1 = b
Therefore, the function rule is:
y = -5x - 1
To find the function rule that relates the values of x and y, we need to examine the relationship between the two sets of numbers.
If we look closely, we can see that when x increases by 1, y decreases by 5. This tells us that there is a constant change of -5 between each pair of corresponding x and y values.
To express this relationship as a function rule, we start with the general form of a linear function: y = mx + b, where m represents the slope and b represents the y-intercept.
Since the change in y is always -5 when x increases by 1, the slope (m) of the function is -5.
Next, we need to find the y-intercept (b). To do this, we can choose any point from the given x and y values. Let's choose the point (-2, 9):
y = mx + b
9 = -5(-2) + b
9 = 10 + b
b = 9 - 10
b = -1
Therefore, the function rule that relates x and y is:
y = -5x - 1