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Linear Equation Project

Linear equations are one of the first types of equations students encounter in their initial foray into algebra. Somewhere in the mix of graphing, plugging in points, and the point-slope formula, students can lose sight of the real-world implications of linear equations, which is why projects that push students out of the classroom have such a pedagogical benefit.
  1. Set Up

    • You're going to need three ropes or long pieces of twine for each group in your class with a weight attached to one of the pieces. You'll also need two stakes, a round ball, a string level and a tape measure for each group.

    Getting Started

    • Go to a hill near your campus. Most school grounds have at least one small hillock on them, but you may need to walk to a nearby park or playground. Have each group put a stake near the top of the slope and set the ball down next to the stake. If the ball doesn't start rolling, a group member should give it a nudge or push. Put the other stake where the ball stops. If the ball rolls out into a flat area past the bottom of the slope, just mark the bottom of the slope.

    Taking Measurements

    • Pull a rope or string tight between the two stakes. Have one group member stand over the stake at the bottom of the slope. Hold a string aloft, tight from the first stake, and level horizontally. Use the string level to ensure the rope stays horizontal. Dangle the string with the weight vertically from the end of the horizontal string so that the weight rests on the stake at the bottom of the slope. Measure the lengths of the horizontal and vertical strings.

    Plotting the Lines

    • Go back to the classroom and have students imagine the y-value of the lower stake as zero, so the stake is resting at the origin on graph paper. Have students plot the "point" for the higher stake. For example, if the higher stake is 48 inches higher and 72 inches away horizontally, they could plot that point at (72, 48) or (6, 4) if they want to use feet. Then have them draw a line between those two points and use those points to come up with the equation of that line.

    Finding the Equation

    • The standard linear equation form is y = mx + b, where m is the slope of the line (the rapidity with which it rises or falls) while b stands for the y-intercept, where the line crosses the y-axis. We defined that point as (0,0) earlier, so b=0 for this line. It remains to find m. To find the slope, plug point values into this formula: m = (y2-y1)/(x2-x1). In this case, (4-0)/(6-0), or 4/6, or 2/3. The equation for this line is y = (2/3)x + 0, or y = (2/3)x.

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