Relating Linear Equations and their Graphs
- Let’s connect functions to features of their graphs.
10.1: Notice and Wonder: Features of Graphs
Here are graphs of \(y=2x+5\) and \(y=5 \boldcdot 2^x\).
What do you notice? What do you wonder?
10.2: Making Connections
- 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.
- \(y = 8\)
- \(y = 3x - 2\)
- \(x + y = 6\)
- \(0.5x = \text-4\)
- \(y = x\)
- \(\text- \frac23 x = y\)
- \(12 - 4x = y\)
- \(x - y = 12\)
- \(2x + 4y = 16\)
- \(3x = 5y\)
- 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?
10.3: Connecting Equations and Graphs
- Without substituting any values for \(x\) and \(y\) or using technology, decide whether graph A could represent each equation, and explain how you know.
- \(4x = y\)
- \(x - 8 = y\)
- \(\text-5x = 10y\)
- \(3y - 12= 0\)
- Write a new equation that could be represented by:
- Graph D
- Graph F
- On this graph, \(x\) represents minutes since midnight and \(y\) represents temperature in degrees Fahrenheit.
- Explain what the intercepts tell us about the situation.
- Write an equation that relates the two quantities.