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Understanding Linear Equations: Rate of Change and Functions

Learn how to use linear equations as a rate of change and understand functions with y=mx+b. Explore examples, slope interpretation, and practical applications to master the concept.

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Understanding Linear Equations: Rate of Change and Functions

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  1. Linear Equations as Rate of Change 3.5

  2. Function • Think of y=mx+b as a machine. You put a number in the machine, and it gives you a new number out. This is called a function

  3. X is always the input • Y is always the output

  4. Example y=10+2x

  5. You try • Complete the table below. • y=20-x

  6. Slope is the rate of change • Slope is how fast the function is changing. • Example: if you are driving, your speed would be the slope.

  7. Example • What is the rate of change? • What is the output when the input is 0? Answer: slope = 3 Output is 4 when input is 0.

  8. “Ms.Farley, when would we ever use this!?” • It is one thing to be able to plug numbers into an equation. It is another thing to use an equation in a real problem. That’s what we are going to practice now. • WARNING: this requires you to THINK. Get ready.

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