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 this table, we need to examine how the input (x-values) and output (y-values) are related. We can see that as x increases by 2, y decreases by 1. This suggests that there is 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 (rate of change) and b is the y-intercept (the value of y when x is 0).
Using the values from the table, we can find m by taking the difference in y-values over the difference in x-values:
m = (y2 - y1)/(x2 - x1) = (1 - 2)/(2 - 0) = -1/2
To find b, we can use any point on the line. Let's use (0, 2):
y = mx + b
2 = (-1/2)(0) + b
b = 2
Therefore, the function rule for this table is:
y = -1/2x + 2
the slope is -1/2, so
y = -1/2 x + b
since y(0) = 2,
y = -1/2 x + 2
Certainly! Using the values from the table, we can find the slope (rate of change) of the function as:
slope = (change in y) / (change in x)
slope = (1 - 2) / (2 - 0)
slope = -1/2
Now that we know the slope of the function, we can write the function rule in the form y = mx + b, where m is the slope and b is the y-intercept. To find the y-intercept, we can use any point on the line. Let's use (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
Yes, that is correct! Good job!
Thank you!
Could you write a function rule?
To write a function rule from a table, you need to identify the pattern or relationship between the input values (x) and the corresponding output values (y). Let's analyze the given table:
x | 0 | 2 | 4 | 6
y | 2 | 1 | 0 | -1
Looking at the table, we can observe that as the values of x increase by 2 each time, the values of y decrease by 1 each time. This pattern suggests that there is a linear relationship between x and y.
To find the function rule, we can use the slope-intercept form of a linear equation: y = mx + b. Here, m represents the slope, and b represents the y-intercept.
To calculate the slope (m), we can choose any two corresponding points from the table. Let's use (0, 2) and (2, 1):
m = (y₂ - y₁) / (x₂ - x₁) = (1 - 2) / (2 - 0) = -1 / 2
So, the slope (m) is -1/2.
Next, let's find the y-intercept (b). To do this, we can substitute the coordinates of one point into the equation and solve for b. Let's use the point (0, 2):
y = mx + b
2 = (-1/2)(0) + b
2 = b
Therefore, the y-intercept (b) is 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