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**5-1: Relating Graphs to Events**

Essential Question: How would you draw a graph representing your commute?

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**5-1: Relating Graphs to Events**

You can use an equation, an inequality, or a proportion to make a statement about a variable. You can use a graph to show the relationship between two variables. For example, you can use a graph to show how a quantity changes over time. Example 1: Interpreting Graphs One student walks and takes a bus to get from school to home each day. The graph below shows the student’s commute by relating the time the student spends commuting and the distance he travels Walking (distance increases slowly) Walking (distance increases slowly) Riding the bus (distance increases quickly) Waiting for the bus

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**5-1: Relating Graphs to Events**

Your Turn The graph below shows a trip from home to school and back. The trip involves walking and getting a ride from a neighbor. Label each section. At School (no distance change) Riding the car (distance changes quickly) Walking (distance changes slowly) Waiting (no distance change)

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**5-1: Relating Graphs to Events**

In the first example, distance, which is on the vertical (up/down) axis, depends on time, which is on the horizontal (left/right) axis. When one quantity depends on another, show the dependent quantity on the vertical axis. Example 2: Sketching a Graph A plane is flying from New York to London. Sketch a graph of the plane’s altitude during the flight. Label each section.

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**5-1: Relating Graphs to Events**

Your Turn Sketch a graph of the distance from a child’s feet from the ground as the child jumps rope.

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**5-1: Relating Graphs to Events**

Assignment Worksheet #5-1 Problems 1 – 12 (all)

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EXAMPLE 1 Find a positive slope Let (x 1, y 1 ) = (–4, 2) = (x 2, y 2 ) = (2, 6). m = y 2 – y 1 x 2 – x 1 6 – 2 2 – (–4) = = 4 6 2 3 = Simplify. Substitute.

EXAMPLE 1 Find a positive slope Let (x 1, y 1 ) = (–4, 2) = (x 2, y 2 ) = (2, 6). m = y 2 – y 1 x 2 – x 1 6 – 2 2 – (–4) = = 4 6 2 3 = Simplify. Substitute.

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