Final answer:
Option B. To find the equation of the secant line on the interval [0, 2], determine the slope using the formula m = (f(b) - f(a)) / (b - a). Then use the point-slope form of a line to find the equation, y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope. The equation of the secant line is y = -x + 2.
Step-by-step explanation:
To find the equation of the secant line on the interval [0, 2], we need to find the slope of the secant line first. The slope of a secant line is given by the formula: m = (f(b) - f(a)) / (b - a), where a and b are the endpoints of the interval and f(x) is the given function.
In this case, a = 0, b = 2, and f(x) = x² - 3x + 2. Plugging these values into the formula, we get: m = (f(2) - f(0)) / (2 - 0). Evaluating f(2) and f(0), we get: m = (2² - 3(2) + 2 - 0² + 3(0) - 2) / 2. Simplifying, we have: m = (4 - 6 + 2) / 2. Therefore, the slope of the secant line is -1.
Now we can use the point-slope form of a line to find the equation. We can choose any point on the line, but let's use (0, f(0)) = (0, 2) as it's given. The point-slope form is given by: y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the slope. Plugging in the values, we get: y - 2 = -1(x - 0). Simplifying, we have: y - 2 = -x or y = -x + 2. Therefore, the equation of the secant line on the interval [0, 2] for the given function is y = -x + 2