How is slope calculated between two points (x₁, y₁) and (x₂, y₂)?

The calculation of slope between two points ((x_1, y_1)) and ((x_2, y_2)) is derived from the definition of slope in the context of a graph, which represents the ratio of the change in the vertical direction (the y-values) to the change in the horizontal direction (the x-values).

Using the coordinates of the two points, you can determine the change in the y-values by subtracting (y_1) from (y_2), which gives you (y_2 - y_1). This expresses how much the y-value changes as you move from the first point to the second. Similarly, the change in the x-values is found by subtracting (x_1) from (x_2), leading to (x_2 - x_1).

Thus, slope is defined mathematically as:

[

\text{slope} = \frac{\text{change in } y}{\text{change in } x} = \frac{y_2 - y_1}{x_2 - x_1}

]

This formula correctly captures the rate of change of y with respect to x between the