1. Algebra 2 Chapter 2.3 Rate of Change and Slope Target Goals: 1.Find the rate of change of data in a real-life situation. 2.Determine the slope (steepness) of a line.

2. Functions and Graphing (review from yesterday) When an equation represents a function, the variable (often x) with values making up the domain is called the INDEPENDENT VARIABLE. The other variable (often y) is called the DEPENDENT VARIABLE. The independent variable is graphed on the horizontal/x-axis. The dependent variable is graphed on the vertical/y-axis.

3. RATE of CHANGE A ratio that compares how much one quantity changes, on average, relative to the change in another quantity. If x is the independent variable and y is the dependent variable, then Rate of Change = change in y = ∆y change in x ∆x

4. Ex 1) In 2004, 56,878 students applied to UCLA. In 2006, 60,291 students applied. Find the rate of change in the number of students applying from 2004 to 2006. Which is the dependent variable? – Number of students Which is the independent variable? – Years

5. Ex 2) You volunteered to take a shift selling Homecoming tickets during your morning study hall. When your shift began at 11:00am, 50 tickets had been sold. At 11:40am, when your shift ended, 84 tickets had been sold. At what rate did you sell Homecoming tickets? Which is the dependent variable? – Number of tickets Which is the independent variable? – Time

6. Ex 3) The graph at the right shows the number of gallons of water in a swimming pool as it is being filled. At what rate is the pool being filled? 330 300 270 240 210 180 150 120 90 60 30 0 2 4 6 8 10 12 Time (minutes) Water (gallons) (7, 252) (3, 108) Which is the dependent variable? – Amount of water Which is the independent variable? – Time

7. SLOPE of a Line The ratio of the change in the y-coordinates to the corresponding change in the x-coordinates The steepness of a line Rate of change = Slope

9. Ex 4) Find the slope of the line that passes through (-1, 4) and (1, -2).

10. Ex 5) Find the slope of the line shown. Pick any 2 points on the line!

11. EXTENSION (you need to know this)!! Slope = UNDEFINED Slope = 0

12. EXTENSION (you need to know this too)!! Rising Line Falling Line Horizontal Line Vertical Line Undefined Slope Positive Slope 0 Slope Negative Slope