which linear function is represented by the graph? \\( f(x) = -2x + 1 \\) \\( f(x) = -\frac{1}{2}x + 1 \\)…

Explanation:

Step1: Recall slope-intercept form

The slope - intercept form of a linear function is (f(x)=mx + b), where (m) is the slope and (b) is the y - intercept. From the graph, we can see that the line crosses the y - axis at ((0,1)), so (b = 1).

Step2: Calculate the slope

The slope (m) between two points ((x_1,y_1)) and ((x_2,y_2)) is given by the formula (m=\frac{y_2 - y_1}{x_2 - x_1}). We can use the points ((0,1)) and ((4,-1)). Let ((x_1,y_1)=(0,1)) and ((x_2,y_2)=(4,-1)). Then (m=\frac{-1 - 1}{4-0}=\frac{-2}{4}=-\frac{1}{2}).

Step3: Identify the function

Since (m =-\frac{1}{2}) and (b = 1), the linear function is (f(x)=-\frac{1}{2}x + 1).

Answer: (f(x)=-\frac{1}{2}x + 1) (the option: (f(x)=-\frac{1}{2}x + 1))