Question

question 9
what is an alternative method to determine the function rules for segments?
using the endpoints and slope formula
using the midpoint of the segment
using the area under the curve
using the derivative of the function

Explanation:

To determine the function rule (equation) for a line segment, we can use the two endpoints. The slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$ (where $(x_1,y_1)$ and $(x_2,y_2)$ are endpoints) finds the slope, and then we can use point - slope form $y - y_1=m(x - x_1)$ to find the equation. The midpoint of a segment doesn't give enough info to find the function rule. The area under the curve is related to integration (for functions, not for finding the equation of a line segment). The derivative is for finding the slope of a tangent (not for finding the equation of a line segment from endpoints). So the correct method is using endpoints and slope formula.

Answer:

A. Using the endpoints and slope formula