Question

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

Answer 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