Final answer:
To find the value of f(x), use the concept of a linear function. Find the slope using the given points, then substitute any x value to find f(x).
Step-by-step explanation:
To find the value of f(x), you can use the concept of a linear function. Since you know that f(17) = 11 and f(7) = 6, you can use these two points to find the slope of the line and then substitute any value of x to find the corresponding value of f(x). First, find the slope:
Slope = (f(17) - f(7)) / (17 - 7)
Slope = (11 - 6) / (17 - 7)
Slope = 5 / 10
Slope = 0.5
Now you can substitute any value of x into the equation:
f(x) = mx + b
f(x) = 0.5x + b
Since you have two points, you can substitute and solve for b:
11 = 0.5(17) + b
11 = 8.5 + b
b = 2.5
Now you can substitute any value of x to find the corresponding value of f(x). For example, if x = 10:
f(x) = 0.5(10) + 2.5
f(x) = 5 + 2.5
f(x) = 7.5