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Writing Functions

Writing Functions. (8.M.F.04) I can write and model a linear relationship using graphs, tables, or a written description. Vocabulary. Linear Equation Independent Variable Dependent Variable Slope Y-intercept. Linear Equation.

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Writing Functions

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  1. Writing Functions • (8.M.F.04) I can write and model a linear relationship using graphs, tables, or a written description.

  2. Vocabulary • Linear Equation • Independent Variable • Dependent Variable • Slope • Y-intercept

  3. Linear Equation • A linear equation is a mathematical statement that represents a straight line when graphed. • A linear equation has a constant rate of change.

  4. Independent Variable • In a linear equation, the independent variableis the one that is not affected by the other variable. • Represented by x, in a linear equation where y = mx + b.

  5. Dependent Variable • In a linear equation, the dependent variableis the one that is affected by the other variable. • Represented by y, in a linear equation where y = mx + b. • Is said to be a function of the independent variable: f(x)

  6. Which one is it? In each situation, determine which is the independent and which is the dependent variable. • The time a student spends studying compared to their score on an exam. • The amount of water in a bucket compared to how fast it is being filled with water. • The height of a tree on a given day.

  7. Slope (Rate of Change) • The term slope is used to describe how steep a line is. • In a given situation, slope is defined by the rate of change. • Represented by m, in a linear equation where y = mx + b.

  8. Y - Intercept • The y-intercept is the point where the graphed line crosses the y-axis (where x=0). • In the particular context of word problems, the y-intercept also refers to the starting value. • Represented by b, in a linear equation where y = mx + b.

  9. Putting it All Together! y-intercept (starting point) Slope (Rate of Change) y = mx + b dependent variable independent variable

  10. Writing Linear Equations Linda begins the year with $200 in her bank account. Each month, she deposits $40. Write an equation for how much money she has in her bank account. What is the independent variable?What is the dependent variable? What is the rate of change? What is the starting point? Months Total Money $40 per month (m) $200 (b)

  11. Writing Linear Equations • Linda begins the year with $200 in her bank account. Each month, she deposits $40. Write an equation for how much money she has in her bank account. Total Money = $40 per month x Months + $200 T = 40M + 200

  12. Writing Linear Equations A parachutist is 500 feet above the ground.After she opens her parachute, she falls ata constant rate of 5 feet per second. Write an equation representing her height over time. What is the independent variable?What is the dependent variable? What is the rate of change? What is the starting point?

  13. Writing Linear Equations A restaurant charges $150 for a room and $10 per person for food and drinks. Write an equation representing the total cost to rent a room at this restaurant.

  14. Closure y = 12x + 5 Write a scenario that would represent the above equation.

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