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4 – Linear Equations

  • As a chairlift carries you up a snowy mountainside, you’re anticipating the thrills to come: the icy wind in your face, the exhilarating speed, the other skiers flying past. You may not be thinking in terms of linear equations—but you could be.
  • If you were to plot the chair’s movement on a graph, what would it look like? The more you move forward, the higher you go up.
  • How would the equation change if the mountain were steeper? Would it change if the chair moved faster?
  • What kind of equation would represent the line you create when you ski down?
  • Linear equations can represent slopes that are easy to visualize, such as a hillside, but they can also show relationships between any two variables that create a straight line when plotted on a graph.
  • How does a farmer’s crop production change based on rainfall?
  • How do store profits increase as the holidays approach?
  • How much would you pay for a shirt that’s 20 percent off? How about 25? Or 30?
  • In this unit, you’ll learn about calculating slopes of lines, linear equations and inequalities, and how they can help you solve a variety of real-world problems.

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