Quantitative Math: Graphical and Visual Representations
Question: A man shines a laser beam from a third-story window of a building onto the pavement below. The path of the laser beam is represented by the equation y = -(2/3)x + 30. In this problem, y represents the height above the ground, and x represents the distance from the face of the building. All height and distance measurements are in feet.
A. Use the situation above to complete parts A1 through A5.
1. Find the x-intercept and y-intercept of the given equation algebraically, showing all work.
2. Graph the given equation.
- Label each axis of the coordinate plane with descriptive labels.
- Label each intercept as "x-intercept" or "y-intercept" and include the ordered pair.
3. Identify the points on the graph that most accurately represent the following:
- The location of the third-story window as an ordered pair.
- The location where the laser beam hits the ground as an ordered pair.
4. Determine the height of the laser beam 30 feet away from the face of the building.
a. Explain the process used to solve this problem algebraically or graphically, showing all work.
5. Determine which quadrant(s) is(are) relevant to this problem.
a. Explain whether the graph is a reasonable visual representation of the path of the laser beam, based on attributes of the story problem and the nature of the graph.
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