Ontario Mathematics Proficiency Practice Test

The formula for finding the slope of a line given two points is derived from the concept of change in vertical distance (rise) over change in horizontal distance (run). When you have two points, typically represented as \((x_1, y_1)\) and \((x_2, y_2)\), the slope represents how steep the line is between these two points.

Using the formula \( \text{Slope} = \frac{(y_2 - y_1)}{(x_2 - x_1)} \), we can see that the numerator, \(y_2 - y_1\), represents the change in the y-coordinates (the vertical change), while the denominator, \(x_2 - x_1\), represents the change in the x-coordinates (the horizontal change). This provides a measure of how much the y-value increases or decreases as the x-value increases, capturing the concept of slope effectively.

The other options do not align with the proper definition of slope. For instance, swapping the positions of \(x\) and \(y\) in the formula or using them incorrectly will not yield the correct measure of slope between two points. Thus, the first option accurately defines