Lesson 10

Here are graphs of \(y=2x+5\) and \(y=5 \boldcdot 2^x\).

What do you notice? What do you wonder?

1. Here are some equations and graphs. Match each graph to one or more equations that it could represent. Be prepared to explain how you know.

   

   

   • \(y = 8\)
   • \(y = 3x - 2\)
   • \(x + y = 6\)
   • \(0.5x = \text-4\)
   • \(y = x\)

   • \(\text- \frac23 x = y\)
   • \(12 - 4x = y\)
   • \(x - y = 12\)
   • \(2x + 4y = 16\)
   • \(3x = 5y\)
2. Choose either graph D or F. Let \(x\) represent hours after noon on a given day and \(y\) represent the temperature in degrees Celsius in a freezer.
   • In this situation, what does the \(y\)-intercept mean, if anything?
   • In this situation, what does the \(x\)-intercept mean, if anything?

1. Without substituting any values for \(x\) and \(y\) or using technology, decide whether graph A could represent each equation, and explain how you know.
   1. \(4x = y\)
   2. \(x - 8 = y\)
   3. \(\text-5x = 10y\)
   4. \(3y - 12= 0\)
2. Write a new equation that could be represented by:
   1. Graph D
   2. Graph F
3. On this graph, \(x\) represents minutes since midnight and \(y\) represents temperature in degrees Fahrenheit.
   1. Explain what the intercepts tell us about the situation.
   2. Write an equation that relates the two quantities.