How do you know what 1400 and -350 mean in the context of the scenario? A pool is being emptied. The equation to model the remaining water (W) at time (t) is W = 1400 – 350t

In this lesson you will learn how to interpret the rate of change and the y-intercept in context by examining each of the four representations.

Let’s Review Rate of change (slope) x (days late) y (late fees) 1$0.50 2$1.00 3$1.50 4$2.00 = – Initial value (y-intercept) = 0

Let’s Review A Common Mistake Suppose a car is traveling 35 miles per hour. An equation could be D = 35h, where D is distance after h hours. What does 35 mean within the context of the scenario? The car goes 35 miles. Incorrect ! The car travels 35 miles for every hour that passes.

Let’s Review Core Lesson A 1400 gallon pool is being emptied at a rate of 350 gallons per hour. W = -350T T (hours) W (remaining gallons)

Let’s Review Core Lesson Rate of change (slope) = Initial value (y-intercept) = Meaning: The pool is losing 350 gallons of water every hour. Meaning: The pool has 1400 gallons before it begins to drain.

In this lesson you have learned how to interpret the rate of change and the y- intercept in context by examining each of the four representations.

Let’s Review Guided Practice A car rental agency charges $30 plus $0.25 per mile for each mile driven. C = m Identify the slope and y-intercept in each representation. Explain the meaning of each. m (miles) C (cost) 0$30 4$31 8$32 12$33

Let’s Review Extension Activities Show an image of a restaurant price board or menu. -Are the prices slopes or y-intercepts? -What does each mean as it pertains to the restaurant? -There is an unseen value for each of the prices, what is it (slope or y-intercept)? -What does the unseen value mean as it pertains to the restaurant?

Let’s Review Extension Activities Think of a situation pertaining to your life that would have a slope and y-intercept. Share the situation, slope, y-intercept, and meaning within the situation.

Let’s Review Quick Quiz A restaurant charges $150 for a room and $10 per person for food and drinks. What is the slope and what does it mean in the context of the scenario? a) Total increases $10 for the room cost. b) Total increases $10 for every added person c) Total is $150 for the room cost. d) Total is $150 for every added person.

Let’s Review Quick Quiz A restaurant charges $150 for a room and $10 per person for food and drinks. What is the y-intercept and what does it mean in the context of the scenario? a) Total is $10 with zero people attending. b) Total increases $10 for every added person c) Total is $150 with zero people attending. d) Total is $150 for every added person.