Understand the connection between similar triangles and slope of a line by using ratios of corresponding sides of the triangles

Big Ideas: A line has a well-defined slope; that is, the ratio between the rise and run for any two points on the line is always the same. This is because any two right triangles with hypotenuses on the line must necessarily be similar. The equation for a line can be written in the form y = mx or y = mx + b, where m represents the rate of change for the independent variable x, and b (called the initial value) represents the value of the dependent variable y when the value of x is zero. This task is designed to help students understand that the slope of a line is uniform throughout the line because any right triangles constructed with their hypotenuses on the line will be similar. Students will construct triangles and use what they know about proportions to create this understanding, and they will recreate the demonstration and explanation without scaffolding during formative assessment. Vocabulary: rate of change, similar triangles, slope, corresponding sides Special Materials: graph paper rulers