Final answer:
The linear function that passes through (-2,2) and (2,0) is y = (-1/2)x + 1, and the slope between the points as a reduced fraction is -1/2.
Step-by-step explanation:
To find the linear function that passes through the points (-2,2) and (2,0), we need to determine the slope and the y-intercept of the line. First, we calculate the slope using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the given points.
The slope is then (0 - 2) / (2 - (-2)) = -2 / 4 = -1 / 2. With the slope known, we use the point-slope form to find the equation of the line: y - y1 = m(x - x1). Plugging in one of the points and the slope, we get y - 2 = (-1/2)(x + 2). Simplifying, y = (-1/2)x + 1, which is the linear function we are looking for.
Therefore, the equation of the line is y = (-1/2)x + 1, with a slope of -1/2 as a reduced fraction.