Question

The green and the orange triangles drawn on the line are similar. What equation can be used to show that the slope of the line is the same between any two points?

Option 1: Rise 1 and Run 1 = Rise 2 and Run 2
Option 2: Rise 1/Rise 2 = Run 1/Run 2
Option 3: Rise 1⋅Run 1 = Rise 2⋅Run 2
Option 4: Run 1/Rise 2 = Run 2/Rise 1

Answer 1

To show that the slope of a line is consistent between any two points, the equation Rise 1/Rise 2 = Run 1/Run 2 is used, which compares the ratios of the rise and run between two similar triangles on the line.

Step-by-step explanation:

The equation that can be used to show that the slope of the line is the same between any two points is Option 2: Rise 1/Rise 2 = Run 1/Run 2. This is because the slope is calculated by taking the difference in y-value (the rise) divided by the difference in x-value (the run) of two points on a straight line. For similar triangles on the same line, the proportions of their sides must be equal, thus the ratio of the rises must be equal to the ratio of the runs, confirming that the slope is consistent along the line.