Final answer:
To find the equation for f(x) when f(x) is a linear function, substitute the given values f(-4) = 0 and f(5) = -5 into the equation y = mx + b and solve for the slope (m) and y-intercept (b). The equation for f(x) is y = -x + 4.
Step-by-step explanation:
To find an equation for f(x) when f(x) is a linear function, we can use the formula for a line, y = mx + b. Given that f(-4) = 0 and f(5) = -5, we can plug these values into the equation to solve for the slope (m) and the y-intercept (b).
Using the point-slope form of a line, we get:
0 = m(-4) + b
-5 = m(5) + b
Simplifying these equations, we find that m = -1 and b = 4.
Therefore, the equation for f(x) is: y = -x + 4.