Final answer:
The rate of change for the points (2,4) and (5,-2) is calculated using the slope formula and results in a rate of change of -2. This indicates a decrease in y by 2 units for each unit increase in x.
Step-by-step explanation:
The rate of change in Mathematics usually refers to the slope of a line or the derivative in calculus. In this case, the notation (5,-2)/(2,4) suggests a slope calculation, where the first coordinate represents a point in the 2-dimensional plane and the second represents another point. To find the rate of change, we calculate the slope using the formula:
Slope (m) = (y2 - y1) / (x2 - x1)
Where (x1, y1) = (2, 4) and (x2, y2) = (5, -2). We subtract the y-values and the x-values:
m = (-2 - 4) / (5 - 2) = -6 / 3 = -2
Hence, the rate of change for the given points is -2, which means for every unit increase in x, the y value decreases by 2 units.