Final answer:
The question pertains to deriving the equation of a line using the two-point form. The standard two-point formula, which relates the slope of a line to any point on the line to the slope defined by two known points, allows for the derivation of this line equation.
Step-by-step explanation:
The student's query appears to be related to deriving a line equation in two-point form, which is usually written as:
(y - y₁) / (y₂ - y₁) = (x - x₁) / (x₂ - x₁)
This formula is used to derive the equation of a line when two points on the line, with coordinates (x₁, y₁) and (x₂, y₂), are known. The formula expresses that the slope of the line calculated using the two points is the same as the slope calculated at any point (x, y) on the line.
To form the derived equation in two-point form, we essentially align the change in y-values with the change in x-values according to the known coordinates of the two points. This forms a ratio that defines the slope and sets up the linear relationship between variables x and y.