1. ALGEBRA READINESS LESSON 8-5 Warm Up Lesson 8-5 Warm-Up

2. ALGEBRA READINESS LESSON 8-5 Warm Up Lesson 8-5 Warm-Up

3. ALGEBRA READINESS “Slope” (8-5) What is “rate of change” How can you find the “rate of change”? rate of change: a unit rate that tells how fast the dependent variable (y) is changes in relation to the dependent variable (y) – In other words, “x changes _?_ much for every change of 1 in y” Since the independent variable is plotted on the x-axis (the x’s) and the dependent variable is plotted on the y-axis (the y’s), we can find the rate of change by using the following rule: Rule: Since rate of change is a linear function (forms a line when graphed), you can use two point on the line to find the vertical and horizontal changes, such as (x 1, y 1 ) and (x 2,, y 2 ). To find the vertical change, find the difference in the y terms (y 2, - y 1 ), and to find the horizontal change, find the difference in the x terms (x 2, - x 1 ) Example: The following graph shows the altitude of an airplane as it’s coming in for a landing. Find the rate of change.

4. ALGEBRA READINESS The rate of change is, which means the airplane descends feet every second. “Slope” (8-5)

5. ALGEBRA READINESS What is “slope” How can you find the “rate of change”? slope: the rate of change of a line on a graph in a unit rate form (how much the y changes for every 1 change in x) Rule: You only need two points on the line to find slope (just like you do for rate of change). You can either: 1. divide the difference of the y values by the difference of the x values or 2. simply divide the rise (vertical distance between the two points) by the run (horizontal distance between the two points) to find slope as in the following example: Note: When using the subtraction method, make sure you start with the same point for the y’s on top and the x’s on the bottom. Example: Find the slope of the line. “Slope” (8-5)

6. ALGEBRA READINESS How do you determine whether a slope (the rate of change) is positive, negative, zero, or undefined (impossible)? can you tell if a slope is positive, negative, 0 (no slope), or undefined (impossible)? “Slope” (8-5)

7. ALGEBRA READINESS slope = rise run Find the slope of the line. –4 2 = Substitute the rise and run. = – 2 Simplify. The slope of the line is –2. Slope LESSON 8-5 Additional Examples

8. ALGEBRA READINESS Find the slope of the line that contains the points (1, 3) and (–2, 2) slope = change in y-coordinates change in x-coordinates = 3 – 2 1 – (–2) Subtract the coordinates of the second point from those of the first. 1313 = Simplify. Slope LESSON 8-5 Additional Examples

9. ALGEBRA READINESS slope = rise run Find the slope of each line. a. 4 – 1 0 – 2 = = 3 –2 = – 3232 The slope of the line is –. 3232 Slope LESSON 8-5 Additional Examples

10. ALGEBRA READINESS The slope of the line is 2. slope = rise run b. (continued) = 2 –1 – 1 –2 – (–1) = = –2 –1 Slope LESSON 8-5 Additional Examples

11. ALGEBRA READINESS slope = y 2 – y 1 x 2 – x 1 The slope of EF is –. 1515 Find the slope of the line through E(3, –2) and F(–2, –1). Substitute (–2, –1) for (x 2, y 2 ) and (3, –2) for (x 1, y 1 ). – 1 – (–2) –2 – 3 = = – 1515 = 1 –5 Simplify. Slope LESSON 8-5 Additional Examples

12. ALGEBRA READINESS = 0 2 – 2 1 – (–4) = Substitute (1, 2) for (x 2, y 2 ) and (–4, 2) for (x 1, y 1 ). slope = y 2 – y 1 x 2 – x 1 The slope of the horizontal line is 0. Find the slope of each line. a. = 0 5 Simplify. Slope LESSON 8-5 Additional Examples

13. ALGEBRA READINESS Division by zero is undefined. The slope of the vertical line is undefined. b. (continued) Substitute (2, 1) for (x 2, y 2 ) and (2, –4) for (x 1, y 1 ). = 1 – (–4) 2 – 2 = 5 0 Simplify. slope = y 2 – y 1 x 2 – x 1 Slope LESSON 8-5 Additional Examples

14. ALGEBRA READINESS 1. Find the slope of each line. 2. the line that passes through the points (1, 3) and (2, 6) 3. the line that passes through the points (–3, 4) and (3, –5) 2 3 3232 – Slope LESSON 8-5 Lesson Quiz