Final answer:
To write a linear function, we find the slope and substitute it into the formula y = mx + b using the given points. With f(5) = -1 and f(0) = -5, the linear function is y = (4/5)x - 9/5.
Step-by-step explanation:
To write a linear function with given points f(5) = -1 and f(0) = -5, we can use the formula for the equation of a line, which is y = mx + b. First, we find the slope (m) by using the formula (y2 - y1) / (x2 - x1). Plugging in the given points (5, -1) and (0, -5), the slope is (-1 - -5) / (5 - 0) = 4/5. Next, we substitute the slope and one of the points into the formula, yielding y = (4/5)x - 9/5. This is the linear function.
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