Question

Create a linear function for the table of values. Use
form. Show all your work.
0 3
1
3 1
6 −1

Answer 1

We want a linear function y = mx + b that fits the points (0, 3), (3, 1), (6, −1).

1. Find the slope m using (0,3) and (3,1):
m = (1 − 3)/(3 − 0) = −2/3.

2. Use (0,3) to find b (since x=0 gives b directly):
b = 3.

3. So the linear function is
y = (−2/3)x + 3.

4. (Optional) Find the missing value at x = 1:
y(1) = (−2/3)(1) + 3 = 3 − 2/3 = 7/3.

Check: y(6) = (−2/3)(6) + 3 = −4 + 3 = −1, which matches the table.