Question

how is the slope of the blue segment determined? using the midpoint formula; by measuring the angle with the x - axis; by calculating the change in y over the change in x; by guessing

Explanation:

The slope of a line segment (or a line) is defined as the ratio of the change in the y - coordinates (Δy) to the change in the x - coordinates (Δx) between two points on the segment. The midpoint formula is used to find the midpoint between two points, not the slope. Measuring the angle with the x - axis is related to finding the slope using trigonometry (slope = tan(θ) where θ is the angle with the x - axis), but the fundamental definition of slope is Δy/Δx. Guessing is not a valid method to determine the slope. So the correct way to determine the slope is by calculating the change in y over the change in x.

Answer:

Orange. By calculating the change in y over the change in x