# Algebra

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SUBDOMAIN 212.1 - NUMERACY, ALGEBRA, & GEOMETRY Competency 212.1.2: Solving Algebraic Equations - The graduate solves algebraic equations and constructs equations to solve real-world problems. Introduction: An important element of learning is to connect mathematical concepts with physical concepts. Graphical representations of mathematical functions will allow you to visualize the meaning and power of mathematical equations. The power of computer programs and graphing calculators provide a more thorough connection between algebraic equations and visual representation, which will increase appreciation and understanding of mathematical language. In this task, you will be making connections between algebraic equations and graphical representations. You will use the following situation to complete your task: 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. Task: 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.…...

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