Slope and triangle similarity

The  exercise appears under the 8th Grade Math Mission. This exercise uses the KA graphing interface and similar triangles to understand the slope of linear functions.

Types of Problems
There are two types of problems in this exercise:


 * 1) Select the triangles that are similar: This problem provides a picture of a coordinate plane and many points. The student is asked to select all triangles that are similar to a given triangle based on the picture.Sats1.png
 * 2) Find the slope and write the equation: This problem provides a coordinate plane with some labeled points. The student is asked to determine a ratio that is the slope and use it to find the equation of the line.Sats2.png

Strategies
Knowledge of graphing lines and the many forms of a line is useful for performing this exercise.
 * 1) The slope of a line is constant.
 * 2) On the first type of problem, mentally drawing the triangle and recognizing which have hypoteni that lie on the line is an efficient method.
 * 3) Any fashion to find the equation of a line is useful for the second type of problem.
 * 4) Lines that go through the origin always have slope of y/x (for any (x,y) that lies on the line) and a y-intercept of zero.

Real-life applications

 * 1) These types of problems can show up on SATs and other standardized tests.
 * 2) Linear equations show up often in business and many of the sciences.