# 5 6 Slope and Rates of Change Slope

- Slides: 9

5 -6 Slope and Rates of Change Slope • How did we define slope yesterday? • When looking at a graph to determine if the slope is positive, negative, zero, or undefined what direction should we look? • I want to find the “rise over run” of a line what should I find first on the line? • Explain what we mean by “rise” and “run”. • How might we encounter slope in the real world?

5 -6 Slope and Rates of Change The slope of a line is a measure of its steepness and is the ratio of rise to run: y Run Rise x If a line rises from left to right, its slope is positive. If a line falls from left to right, its slope is negative. A horizontal line has a zero slope. A vertical line has an undefined slope.

5 -6 Slope and Rates of Change You can graph a line if you know its slope and one of its points.

5 -6 Slope and Rates of Change Additional Example 2 B: Using Slope and a Point to Graph a Line 2 Use the slope 1 and the point (– 1, – 1) to graph the line. rise = 1 run 2 From point (– 1, – 1) move 1 unit up and 2 units right. Mark the point where you end up, and draw a line through the two points. y 4 2 – 4 – 2 0 – 2 – 4 ● x 2 4

5 -6 Slope and Rates of Change Check It Out: Example 2 A Use the slope – 2 3 and the point (2, 0) to graph the line. rise = -2 or 2 run 3 -3 From point (2, 0) move 2 units down and 3 units right, or move 2 units up and 3 unit left. Mark the point where you end up, and draw a line through the two points. y 4 ● 2 – 4 – 2 0 – 2 – 4 x 2 4 ●

5 -6 Slope and Rates of Change Additional Example 3: Identifying Rates of Change in Graphs Tell whether each graph shows a constant or variable rate of change. A. B. The graph is nonlinear, so the rate of change is variable. The graph is linear, so the rate of change is constant.

5 -6 Slope and Rates of Change Lesson Quizzes Standard Lesson Quiz for Student Response Systems

5 -6 Slope and Rates of Change Lesson Quiz for Student Response Systems 1. Tell whether the slope is positive or negative. Then identify the slope. A. positive; 1 B. positive; 2 C. negative; – 1 D. negative; – 2

5 -6 Slope and Rates of Change Lesson Quiz for Student Response Systems 3. Which of the following graphs represents a variable rate of change? A. B.

- Variable rate of change
- Ratios rates and unit rates
- Equivalent ratios definition
- Ratios rates and unit rates
- Ratios rates and unit rates
- Rates of change in the natural and social sciences
- How to find average rate of change from a graph
- Linear models and rates of change
- What is slope decline
- Converting point slope to slope intercept