can you help me out with this one Ms. Sue
Explain how to write a function rule from the table below. Then write the function rule.
x 2 4 6
y 1 0 -1
y = mx + b
f(x) = 2m + b = 1
f(x) = 4m + b = 0
f(x) = 6m + b = -1
-1(2m + b = 1)
4m + b = 0
-2m -b = -1
4m + b = 0
2m = -1
m = -1/2
2(-1/2) + b = 1
-1 + b = 1
-1+ 1 + b = 1 + 1
b = 2
y = mx +b
y = -1/2x + 2
y = mx + b
f(x) = 2m + b = 1
f(x) = 4m + b = 0
f(x) = 6m + b = -1
-1(2m + b = 1)
4m + b = 0
-2m -b = -1
4m + b = 0
2m = -1
m = -1/2
2(-1/2) + b = 1
-1 + b = 1
-1+ 1 + b = 1 + 1
b = 2
y = mx +b
y = -1/2x + 2
thank yoooooooooo!
Is this right?
Certainly! To write a function rule from a table, we need to examine the relationship between the values of x and y. We can see that as x increases by 2 each time, y decreases by 1. This tells us that there is a constant rate of change, which means our function will be linear.
To write the function rule, we need to express the relationship between x and y algebraically. We know that as x increases by 2, y decreases by 1. This means the rate of change is -1/2.
To start, we write the general form of a linear function as y = mx + b, where m is the slope and b is the y-intercept. Since we have the slope, we can substitute it into the equation:
y = -1/2x + b
To find the y-intercept, we can substitute the values of x and y from one of the points in the table. Let's choose the first point (2, 1):
1 = -1/2(2) + b
Simplifying the equation, we get:
1 = -1 + b
Adding 1 to both sides:
b = 2
Now that we have the slope (m = -1/2) and the y-intercept (b = 2), we can write the function rule:
y = -1/2x + 2