Step 1) Draw a vertical line through -1 on the x axis. This vertical line crosses through the point (-1,-5) which is a point on the hyperbola.
Step 2) Draw a vertical line through 1 on the x axis. This line crosses the hyperbola at (1,5).
Step 3) Find the slope of the line through the two points (-1,-5) and (1,5) using the slope formula
m = (y2 - y1)/(x2 - x1) m = (5 - (-5))/(1 - (-1)) m = (5 + 5)/(1 + 1) m = 10/2 m = 5
The slope of the line is 5. This is the same as saying the average rate of change is 5. The average rate of change is over the interval [-1,1] which is the same as the interval -1 <= x <= 1
Note: writing "<=" without quotes means "less than or equal to".
