We need to start by finding the slope of the given line, since a line parallel to it will have the same slope. Then we need to solve for y in the given equation;
- 2 x + 4 y = 8
add 2x to both sides
4 y = 2 x + 8
divide both sides by 4 to isolate y
y = 1/2 x + 2
Then, the slope we are looking for is "1/2"
Now we write the equation of the parallel line we are trying to find, in "point slope form", using the point (-5, -1) we want to have on the line:
y = m (x - x1) + y1
replacing m with our slope 1/2, x1 with -5, and y1 with -1:
To solve this we are going to use the average rate of change formula: where is the average rate of change of the function is the position function evaluated at is the position function evaluated at is the first point in the interval is the second point in the interval
We can infer for our problem that the first point is 3 and the second point is 6, so and . Lets replace those values in our formula:
We can conclude that the average rate of change of the function f(x) = 1 x - x2 - 2 for <span>3 ≤ x ≤ 6 is -8</span>