Question

So write a linear function f(x) with the values f(3) = - 1 and f(6) = 1

Answer 1

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

$1 = (\frac{2}{3})6 +b$

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