Answer :
Final answer:
To find f(6) for the linear function f, calculate the slope using the given points, find the y-intercept, and use them to determine the value of f at x=6. Therefore, the correct answer is b. 28, but with the opposite sign due to the negative slope.
Explanation:
We are given a linear function f with two values: f(1) = -3 and f(-1) = 7. To find f(6), we first need to determine the slope of the function, since a linear function has the form f(x) = mx + b where m is the slope and b is the y-intercept.
To find the slope m, we use the formula m = (f(x2) - f(x1)) / (x2 - x1). Plugging in our values, we get:
m = (f(-1) - f(1)) / (-1 - 1) = (7 - (-3)) / (-2) = 10 / (-2) = -5.
Now that we have the slope, we need to find the y-intercept b. We can use one of our known points to solve for b. Let's use f(1) = -3:
-3 = (-5)(1) + b
b = -3 + 5 = 2.
With both the slope and y-intercept known, the function can be written as f(x) = -5x + 2. We can now find f(6):
f(6) = -5(6) + 2 = -30 + 2 = -28.
