Final answer:
The slope of the secant line for the function f(x) = x² - 8 between x = -2 and x = 6 is calculated by finding the y-values at these points and using the slope formula. It results in a slope of 4.
Step-by-step explanation:
To determine the slope of the secant line between two points on the function f(x) = x² - 8, you need to calculate the difference in the y-values of the function at these two x-values, divided by the difference in the x-values. This is also known as the rise over run formula.
First, we need to find the y-values for x = -2 and x = 6. Substituting these x-values into the function gives us:
- f(-2) = (-2)² - 8 = 4 - 8 = -4
- f(6) = (6)² - 8 = 36 - 8 = 28
Now we have two points: Point 1 (-2, -4) and Point 2 (6, 28).
Next, we calculate the slope using the formula:
Slope (Δy/Δx) = (y2 - y1) / (x2 - x1)
Slope = (28 - (-4)) / (6 - (-2))
Slope = 32 / 8
Slope = 4
Therefore, the slope of the secant line between x = -2 and x = 6 for the function f(x) = x² - 8 is 4.