Answer:
f(x) = -2/3x - 3
Step-by-step explanation:
Given the values f(3) = - 1 and f(6) = 1
We're essentially provided (3, -1) and (6, 1).
Let (x1, y1) = (3, -1)
(x2, y2) = (6, 1)
Substitute these values into the slope formula:
m = (y2 - y1)/(x2 - x1)
m = [1 - (-1)]/(6 - 3)
m = (1 + 1) / 3
m = 2/3
Next, we need to find the y-intercept. Use one of the points, (6, 1), and the slope, m = 2/3, and substitute these values into the slope-intercept form to solve for the y-intercept, b:
y = mx + b
[tex]1 = (\frac{2}{3})6 +b[/tex]
1 = 4 + b
Subtract 4 from both sides to solve for b:
1 - 4 = 4 - 4 + b
-3 = b
Therefore, the linear function is: f(x) = -2/3x - 3
