Explain how to write a function rule from the table below. Then write a function rule.
x 0 2 4 6
y 2 1 0 –1
To write a function rule from the table, we need to determine how the input (x) is related to the output (y). We can see that as x increases by 2, y decreases by 1. This tells us that the function has a constant rate of change of -1/2.
To write the function rule, we can use the slope-intercept form of a linear equation: y = mx + b, where m is the slope and b is the y-intercept. Since the function has a slope of -1/2, we can plug that in: y = (-1/2)x + b. To find b, we can choose any point on the table and substitute the x and y values. For example, if we choose (0,2), we get:
2 = (-1/2)(0) + b
b = 2
So the function rule is:
y = (-1/2)x + 2
Sure, I can help you with that! Writing a function rule involves identifying the relationship between the input, which is represented by x, and the output, which is represented by y. Let's take a look at the table:
From the table, we can observe that as x increases by 2, y decreases by 1. So, we can conclude that the relationship between x and y is linear, with a constant rate of change of -1.
To write the function rule, we can start by determining the initial value of y (y-intercept). From the table, when x = 0, y = 2. This tells us that when x is 0, y starts at a value of 2.
So, the function rule for this table can be written as:
y = -x + 2
This means that for any given value of x, you can find the corresponding value of y by substituting the value of x into the function rule and solving for y.
To write a function rule from a table, we need to identify the relationship between the values of x and y.
Looking at the table, we can observe that as x increases by 2, y decreases by 1. This suggests that there is a linear relationship between x and y.
To find the function rule, we need to determine how the value of y is calculated based on the value of x.
Let's start with the initial value or y-intercept. Looking at the table, when x is 0, y is 2. This gives us the y-intercept, which is 2.
Next, we need to determine the slope. The slope is the rate at which y changes with respect to x. From the table, we can see that for every increase of 2 in x, y decreases by 1. Thus, the slope is -1/2.
Therefore, the function rule for this table is:
y = -1/2x + 2
To write a function rule from a table, we need to identify the pattern or relationship between the values in the x-column and the corresponding values in the y-column.
Looking at the table, we can observe that as the values in the x-column increase by 2 (from 0 to 2, 2 to 4, and so on), the values in the y-column decrease by 1 (from 2 to 1, 1 to 0, and so on). This suggests a linear relationship.
To write a function rule, we can use the formula for a linear function: y = mx + b, where m represents the slope of the line and b represents the y-intercept.
Step 1: Find the slope (m):
To find the slope, we can choose any two distinct points from the table and calculate the change in y divided by the change in x. Let's select the points (0, 2) and (2, 1):
m = (y2 - y1) / (x2 - x1)
= (1 - 2) / (2 - 0)
= -1/2
Step 2: Find the y-intercept (b):
To find the y-intercept, we can substitute the coordinates of one of the points into the equation y = mx + b and solve for b. Let's use the point (0, 2):
2 = (-1/2)(0) + b
2 = b
Step 3: Write the function rule:
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
Therefore, the function rule for the given table is y = -1/2x + 2.