Lesson 10

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

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?

10.3: Connecting Equations and Graphs

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.