Unit 2 Day 2: Slope as a Rate of Change Essential Questions: What are the four types of slope and what do they look like? How do you find the slope of a line using a graph or two ordered pairs?

Vocabulary Slope: the steepness of a line, represented by the letter m. Rate of Change: when one quantity changes at a constant rate (example: hourly pay). Slope is a rate of change. Slope Formula: = = change in y change in x y2 - y1 x2 - x1 rise run

Types of Slope Positive Negative Zero Undefined

rise m = run Type: positive negative 2 1 -1 2 = 2 undefined zero Example 1: Using the graphs below, classify the slope of the line as positive, negative, zero or undefined. Then find the value of the slope. m = rise run Type: positive negative 2 1 -1 2 = 2 undefined zero undefined

What is the common difference for y as x increases by 1? Example 2: Create the table of values to graph the equation y = 3x - 2. x y = 3x - 2 y (x , y) -2 y = 3(-2) - 2 -8 (-2 , -8) -1 y = 3(-1) - 2 -5 (-1 , -5) y = 3(0) - 2 (0 , -2) 1 y = 3(1) - 2 (1 , 1) 2 y = 3(2) - 2 4 (2 , 4) What is the common difference for y as x increases by 1? The common difference is +3 (this is the SLOPE!)

Using the Slope Formula y2 - y1 x2 - x1 y2 = y-coordinate of 2nd point y1 = y-coordinate of 1st point x2 = x-coordinate of 2nd point x1 = x-coordinate of 1st point It doesn’t matter which point you choose as the 1st point and which one you choose as the second point!

x1 y1 x2 y2 x1 y1 x2 y2 y2 - y1 x2 - x1 4 - 2 3 - (-2) y2 - y1 x2 - x1 Example 3: Find the slope of the line passing through the given points. (-2 , 2) and (3 , 4) (-1 , 2) and (3 , 2) x1 y1 x2 y2 x1 y1 x2 y2 y2 - y1 x2 - x1 4 - 2 3 - (-2) y2 - y1 x2 - x1 2 - 2 3 - (-1) 2 3 + 2 3 + 1 2 5 m = m = 0

x1 y1 x2 y2 x1 y1 x2 y2 y2 - y1 x2 - x1 1 - 4 2 - 2 y2 - y1 x2 - x1 Example 4: Find the slope of the lines passing through the given points. (0 , 0) and (3 , -3) (2 , 4) and (2 , 1) x1 y1 x2 y2 x1 y1 x2 y2 y2 - y1 x2 - x1 1 - 4 2 - 2 y2 - y1 x2 - x1 -3 - 0 3 - 0 -3 -3 3 m = -1 m = undefined

Rate of change: $0.13 per year Example 5: In 2010 the average price for a soda was $0.99. In 2012 the average price for a soda was $1.25. Calculate the rate of change for the price of soda per year. change in price change in time $1.25 - $0.99 2012 - 2010 $0.26 2 years Rate of change: $0.13 per year

Summary Essential Questions: What are the four types of slope and what do they look like? How do you find the slope of a line using a graph or two ordered pairs? Take 1 minute to write 2 sentences answering the essential questions.