A relationship between two variables is linear if one changes at a constant rate relative to the other. Here are a few examples of linear relationships:
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A car driving at 40mph will travel exactly 40 miles for each additional hour
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A lemonade stand that sells cups of lemonade for $0.75/ea will charge exactly $0.75 for each additional glass
We can see linear relationships show up in Tables, Graphs, and Function Definitions:
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fx = 10x + 7
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In Graphs, linear relationships appear as points that form a straight line. These lines have a slope ("rise over run") and a y-intercept (where the line crosses the y-axis, at x=0).
In Tables, linear relationships show up as y-values that change by a constant rate relative to their x-values.
We can define linear relationships using Function Definitions (either in function notation or Pyret code). Linear functions always include a term for the slope and another for the y-intercept.
If you know how to read the slope and y-intercept for Tables, Graphs and Definitions, you can switch back and forth between each representation. This flexibility is good: sometimes it’s just easier to look at a table or a graph, or see the definition!
These materials were developed partly through support of the National Science Foundation,
(awards 1042210, 1535276, 1648684, and 1738598). 
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