1. Section 6-1 Rate of Change and Slope SPI 13A: apply concept of slope to represent rate of change in real-world SPI 22J: determine the slope from the graph of a linear equation (no labels) Objectives: Find rate of change (slope) from tables, graphs, and ordered pairs Rate of Change (slope): the relationship between two quantities that are changing. x coordinatey coordinate domainrange independent variabledependent variable inputoutput Ordered pair: (x, y), (x, f(x)), Function: f(x), y, b(a), h(d), ….etc

2. 1. Vertical change from: A to B: B to C: C to D: 2. Horizontal change from: A to B: B to C: C to D: 3. Ratio of vertical to horizontal: A to B: B to C: C to D: 4. Which section is the steepest? Explain. Investigate Slope (Rate of Change) 1 unit 4 unit 1 unit 3 unit 1/3 4/3 1/3 unit

3. Rate of Change = Vertical change Horizontal change Change in dependent variable Change in Independent variable = For the data in the table, is the rate of change the same for each pair of consecutive mileage amounts? Fee for Miles Driven MilesFee 100$30 150 200 250 $42 $54 $66 1. Find rate of change for each pair: Finding the Rate of Change using a Table 42 - 30 150 - 100 = 12 = 6 50 25 54 - 42 200 - 150 = 12 = 6 50 25 66 - 54 250 - 200 = 12 = 6 50 25 2. Is the rate of change the same? 3. Find the rate of change between the last entry and the first entry. Is the rate of change the same? YES

4. Slope Formula Slope = change in y change in x Slope Formula Slope = y 2 – y 1 x 2 – x 1 One pair of coordinates The other pair of coordinates Using Slope to graph an equation From a known point: Top number is rise: Move up (+) or down (-) Bottom number: Move right Slope is: 3 4

5. Below is a graph of the distance traveled by a motorcycle from its starting point. Find the rate of change. Explain what this rate of change means. The motorcycle is traveling 20 meters each second. Find the Rate of Change (slope) by using two Points Choose two points on the graph (0,0) & (400,20) Using the points (0,0) and (400,20), find the rate of change. Slope = y 2 – y 1 x 2 – x 1 Fill in known values into the slope formula Slope = 400 - 0 20 - 0 Simplify Slope (m) = 400 = 20 20

6. The slope of the line is –. 3232 Slope (m) = rise run Find the slope of the line. = – 3232 = 3 –2 4 – 1 0 – 2 = Find the Slope of the line using the Slope Formula slope formula (m) = y 2 – y 1 x 2 – x 1 y 2 – y 1 x 2 – x 1 Notice the line goes down from left to right. It is a negative slope.

7. slope formula (m) = y 2 – y 1 x 2 – x 1 Find the slope of a line through the points (3, –2) and (–2, –1). Find the slope of the line. slope = Special Slopes y 2 – y 1 x 2 – x 1 2 - 2 -4 - 1 == 0 -5 = 0 y 2 – y 1 x 2 – x 1 -4 - 1 2 - 2 == -5 0 Slope is UNDEFINED

8. Find the Rate of Change (slope) using a Graph Find the rate of change of the data in the graph. slope = y 2 – y 1 x 2 – x 1 200 – 100 4 – 2 = (4, 200) (2, 100) 100 2 = = 50 The automobile is moving at a rate of 50 mph.