Final answer:
To write a linear function with given values, we use the slope-intercept form y = mx + b. Using the given values, we can find the slope and substitute them into the equation to find the linear function.
Step-by-step explanation:
To write a linear function with the values f(2) = 4 and f(5) = -8, we can use the slope-intercept form of a linear function: y = mx + b, where m is the slope and b is the y-intercept.
First, we can find the slope using the formula: m = (y2 - y1) / (x2 - x1). Substituting the given values, we get m = (-8 - 4) / (5 - 2) = -12 / 3 = -4.
Next, we can choose any of the given points, say (2, 4), to substitute into the slope-intercept form. Substituting the values, we get:
4 = -4(2) + b. Solving for b, we have b = 12.
Therefore, the linear function is f(x) = -4x + 12.
Learn more about Writing a linear function