The standard requires students to use triangles between two points on a line and compare the sides to understand that the slope, is the same between any to points on the line. right triangles on a graph to understand the meaning of slope. Although the standard does include the slope formula, students need to connect their understanding of the formula to the points on the graph in relation to the right triangle. Students should understand that slope, m, compares the change in any of the y-values to the change in any of the x-values.
Triangle ABC is similar to triangle CDE.
Explain why the slope of the hypotenuse is the same for both right triangles.
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8.4 Proportionality. The student applies mathematical process standards to explain proportional and non-proportional relationships involving slope. The student is expected to:
(A) use similar right triangles to develop an understanding that slope, m, given as the rate comparing the change in y-values to the change in x-values, (y2 - y1)/ (x2 - x1), is the same for any two points (x1, y1) and (x2, y2) on the same line