Question

Explain how to write a function rule from the table below.
x 0, 2, 4, 6
y 2, 1, 0, -1

Answer 1

the slope is -1/2, so
y = -1/2 x + b
since y(0) = 2,
y = -1/2 x + 2

Answer 2

Thank you!
Could you write a function rule?

Answer 3

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

Answer 4

Yes, that is correct! Good job!

Answer 5

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