explain how to write a function rule from the table below x 0,2,4,6 y 2,1,0,-1
To write a function rule from the given table, you can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.
To find the slope, you need to calculate the change in y over the change in x between any two points on the table. For example, between x = 0 and x = 2, the change in y is 2 - 1 = 1, and the change in x is 2 - 0 = 2. Therefore, the slope is:
m = (change in y) / (change in x) = 1 / 2
Now, you can use the slope and any point on the table to find the y-intercept. Let's use the point (0, 2):
y = mx + b
2 = (1/2) * 0 + b
b = 2
Therefore, the function rule for this table is:
y = (1/2)x + 2
Well, here's a joke for you:
Why did the function go to the party?
Because it wanted to rule the dance floor!
Now, let's figure out the function rule for the table you provided. Looking at the x and y values, we can see that as x increases by 2, y decreases by 1. So, we can say that our function is subtracting 1 for every 2 units of increase in x.
Therefore, our function rule can be written as:
y = 2 - (x / 2)
But remember, this is just based on the given table. Can't guarantee that this rule would hold true for all values!
To write a function rule from a given table, we need to find a general mathematical expression that relates the input values (x) to the output values (y). Let's analyze the given table:
x | 0 | 2 | 4 | 6
y | 2 | 1 | 0 | -1
By observing the table, we can notice that as x increases by 2, y decreases by 1. This suggests that the output (y) is decreasing at a constant rate of 1 for every increase of 2 in the input (x).
To find the function rule, we can express this relationship using the slope-intercept form of a linear equation, which is:
y = mx + b
Here, m represents the slope, and b represents the y-intercept. In our case, the slope (m) is -1/2 (since y decreases by 1 for every increase of 2 in x), and the y-intercept (b) is 2 (the value of y when x = 0).
Therefore, the function rule for the given table is:
y = -1/2x + 2
To write a function rule from a table, we need to find a pattern or relationship between the values of x and y. Here's how you can do that:
1. Look for a pattern:
- Start by examining the values in the y column. Do you notice any patterns or relationships? In this case, we can see that as x increases by 2, y decreases by 1. This suggests a linear relationship between x and y.
2. Determine the rate of change:
- Calculate the rate of change by dividing the change in y by the change in x. In this case, the change in y is -1 (from 2 to 1) and the change in x is 2 (from 0 to 2). So, the rate of change is -1/2.
3. Write the function rule using the slope-intercept form:
- The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept.
- We know that the slope (m) is -1/2 from the rate of change.
- To find the y-intercept (b), we can substitute one of the points from the table into the equation. Let's use the point (0, 2).
- Substitute the values into the equation:
2 = (-1/2)*0 + b
2 = b
4. Write the function rule:
- Now that we have the slope (m) and the y-intercept (b), we can write the function rule. In this case, the function rule is:
y = -1/2x + 2
So, the function rule for the given table is y = -1/2x + 2.