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Understanding the Rate of Change in Linear Relationships and Real-World Applications

The rate of change in a linear relationship indicates the steepness of a line, commonly expressed through concepts like roof pitch and road grade. For instance, a steeper roof allows for snow runoff, while engineers use grades to assess road inclines. In practical scenarios, wheelchair ramp steepness is crucial for safety, requiring a careful balance in rise and run. This exploration explains how to calculate rates of change in various contexts, such as the grade of a road or the hourly wage versus hours worked, highlighting its real-world significance.

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Understanding the Rate of Change in Linear Relationships and Real-World Applications

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  1. Rate of Change

  2. run rise Rate of Change= Rate of Change of a Linear Relationship The rate of change of a linear relationship is the steepnessof the line.

  3. Rates of change are seen everywhere.

  4. The steepness of the roof of a house is referred to as the pitch of the roof by home builders.

  5. Give one reason why some homes have roofs which have a greater pitch. There is less snow build up in the wintertime.

  6. Engineers refer to the rate of change of a road as the grade.

  7. They often represent the rate of change as a percentage.

  8. 100 8 Rate of change = A grade of 8% would mean for every rise of 8 unitsthere is arun of 100 units. = 8%

  9. The steepness of wheelchair ramps is of great importance for safety. 1 12 Rate of change of wheelchair ramp = If the rise is 1.5 m, what is the run? Answer: 18 m because

  10. Determine the rate of change (pitch) of the roof. 3 m 5 m

  11. 3 2 3 3 Determine the rate of change of each staircase.

  12. Determine the rate of change. Which points will you use to determine rise and run? Earnings 4 20 = $5/hr What does this rate of change represent? Number of Hours Worked The hourly wage

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