Question

Listen

Write a linear function f with the values f(-1) = 5 and f(3) = 4.
A function is f(x) =
Previous
1 2 3
4
5
6
7
8
Next

Answer 1

To write a linear function with given values, we calculate the slope and y-intercept. The linear function is f(x) = -1/4x + 19/4.

Step-by-step explanation:

To write a linear function, we need to determine the slope (m) and the y-intercept (b) of the function.

Given that f(-1) = 5 and f(3) = 4, we can calculate the slope using the formula: m = (f(3) - f(-1)) / (3 - (-1)).

Plugging in the values, we get m = (4 - 5) / (3 + 1) = -1/4.

Next, we can use one of the points and the slope to find the y-intercept. Using f(-1) = 5, we can substitute -1 for x and 5 for f(x) in the equation f(x) = mx + b and solve for b.

5 = (-1/4)(-1) + b

5 = 1/4 + b

b = 5 - 1/4 = 19/4.

Therefore, the linear function is f(x) = -1/4x + 19/4.

Learn more about Writing a linear function