Final answer:
To find f(−4), we use the points (0, 2) and (4, 0) to calculate the slope of the line, which is -1/2. With the y-intercept of 2, we form the equation y = -1/2x + 2 and find that f(−4) = 4.
Step-by-step explanation:
To determine f(−4), we need to find the value of the function f(x) at x = −4. According to the given description, the graph of the line passes through the points (0, 2) and (4, 0). We can use these points to find the slope of the line, which is necessary for calculating f(x) at any given x-value.
To calculate the slope (m), we use the formula:
m = (y2 - y1) / (x2 - x1)
By substituting the given points:
m = (0 - 2) / (4 - 0) = -2 / 4 = -1/2
Now we have the slope. The y-intercept is given directly by the point (0, 2), which means b = 2. Using the general form of a straight line equation y = mx + b, we now have:
y = -1/2x + 2
To find f(−4), we simply substitute x = −4 into our equation:
f(−4) = -1/2(-4) + 2 = 2 + 2 = 4
Therefore, f(−4) = 4.