This project, from Digital Lesson, gives students a set of linear equations to graph. When they've finished graphing the lines, they follow the directions to fill in the gaps between the lines in specific colors. The teacher can assess correct graphing by comparing the pattern of "stained glass" that the students create with the answer key pattern.
You'll be taking your class outside to complete this project. Place a stake in the ground at a point on or near the top of a hill, and then climb down to place a second stake near or at the bottom of the hill. String a rope out horizontally from the higher stake, using a level to test the horizontality. Then, bring a string up vertically from the lower stake. Measure the distance from the stakes to the intersection. The horizontal distance will give you the run; the vertical distance will give you the rise (or fall). Divide rise by run to get slope, a crucial part of linear equations.
Using sets of coordinates that you provide, students plot points and connect them with line segments, in a project from The Math Tree. These segments will make the outline of a cartoon character. Using the points and the point-slope formula, students can calculate the equation of each line segment.
Projects like this one posted by the University of Illinois-Urbana/Champaign guide students to explore real-world situations that involve linear equations. Possible topics include burning calories, buying cars and stats from basketball, but you can come up with other linear topics, such as consumer buying habits and the formation of rust. Students collect data and submit graphs.