Explain how to write a function rule from the table below. Then write a function rule.
x: 2, 4, 6
y: 1, 0, -1
please help, I don't know how to find the answer
the function rule tells you how to get y from x
x is increasing by 2, while y decreases by 1
... this means the slope is -1/2
try some values to see if you can find the y-intercept
To write a function rule from a table, you need to identify any patterns or relationships between the values of x and y.
Looking at the table:
x: 2, 4, 6
y: 1, 0, -1
We can see that as the value of x increases by 2 each time, the value of y decreases by 1 each time. Therefore, we can conclude that the function rule is a linear function with a slope of -1 and a y-intercept of 3.
To write the function rule, we use the slope-intercept form of a linear function, which is y = mx + b, where m is the slope and b is the y-intercept.
In this case, the slope is -1 and the y-intercept is 3. The function rule is:
y = -x + 3
So, the function rule for the given table is y = -x + 3.
To write a function rule from the given table, you need to understand the relationship between the values of x and the corresponding values of y.
1. Look for a pattern between the values of x and y in the table. Examine how the values change as x increases.
In this case, as x increases by 2 each time (from 2 to 4 to 6), y is decreasing by 1 each time (from 1 to 0 to -1). This suggests that there is a linear relationship between x and y.
2. Determine the equation of the linear relationship.
You can use the slope-intercept form of a linear equation: y = mx + b, where m represents the slope and b represents the y-intercept.
3. Find the slope (m):
To find the slope, you can choose any two sets of x and y values from the table and calculate the change in y divided by the change in x.
Let's choose the first two sets of values: (2, 1) and (4, 0).
The change in y is 0 - 1 = -1.
The change in x is 4 - 2 = 2.
Divide the change in y by the change in x:
-1 / 2 = -0.5.
So, the slope (m) is -0.5.
4. Find the y-intercept (b):
To find the y-intercept, you can use any point from the table. Let's use the third set of values: (6, -1).
Plug in the values of x and y into the slope-intercept form equation and solve for b:
-1 = -0.5(6) + b
-1 = -3 + b
b = -1 + 3
b = 2.
So, the y-intercept (b) is 2.
5. Write the function rule:
Using the slope (m = -0.5) and the y-intercept (b = 2), the function rule for this table is:
y = -0.5x + 2.
Therefore, the function rule for this table is y = -0.5x + 2.