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Understanding Linear Models and Functions in Mathematics

This educational video dives into modeling linear situations using mathematical phrases, focusing on expressions containing numbers, variables (like x and y), and operations without equal signs. Learn about variables as lowercase letters representing any number and discover the concept of unit rate of change, analyzed through first differences and ordered pairs. Understand how to calculate rates of change and represent them with a denominator of 1. Finally, explore the relationship between inputs, outputs, and functions in mathematics, essential for creating linear models.

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Understanding Linear Models and Functions in Mathematics

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  1. http://www.youtube.com/watch?v=noE1YzvfA08

  2. LT 2.1 I can model linear situations.

  3. Pg. 73

  4. Expression A mathematical phrase that can contain ordinary numbers, variables (x, y) AND an operation (+, -, ÷, x) • It does NOT include an equal (=) sign • Examples: • x + 5 • 8x Variable Lower cased letters that can represent any Number.

  5. Unit Rate of Change Subtract First Differences • Used to determine the unit rate of change • Are determined by calculating the difference between successive points • In other words: • Subtract the first number from the second number. One after the other

  6. Ordered pair = Two numbers written in a certain order. Usually written in parentheses like this: (4,5) Another way… Determine unit rate of change • Calculate the rate of change between any twoordered pairs • Write each rate with a denominator of 1 Note: Use this method when numbers are NOT consecutive, in order. Numerator Denominator 3 5

  7. Rate of Change May be written with fractions that are not simplified Example: 900/0.5 or 1800/1 (see number 9a) Unit Rate of Change MUST be written with a denominator of 1 • Must be the simplified fraction NOTE When the rate of change between all points is constant, the ordered pairs will form a straight line when plotted.

  8. Functions Background Rate of Change • Relates an input to an output • f(x) = … is the classic way of writing a function • Functions have 3 main parts • Input (x) • Rate of change • Output (y)

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