1. Lesson 1.1: Lines AP Calculus Mrs. Mongold

2. Definition of Increment If coordinates change from (x 1, y 1 ) to (x 2, y 2 ) the increments in the coordinates are Δx = x 2 – x 1 and Δy = y 2 - y 1 where Δx and Δy are increments of x and y respectively. Increments can be positive, negative, or zero

3. Finding Increments 1. ( 4, -3) to (2, 5) 2. (5, 6) to (5, 1)

4. Slope Let P 1 (x 1, y 1 ) and P 2 (x 2, y 2 ) be points on a non- vertical line, L. The slope of L is  Line going up hill from L to R has + slope  Line going down hill from L to R has – slope  Horizontal lines have zero slope  Vertical lines have no slope (undefined)

5. Parallel and Perpendicular Lines Parallel lines for equal angles with the x- axis…. i.e. the lines have the same slope Perpendicular lines form 90 0 angles with the each other…. i.e. the lines have opposite reciprocal slopes

6. Parallel Lines ɵ1ɵ1 ɵ2ɵ2 m1m1 m2m2

7. Perpendicular Lines m1m1 m2m2 A C B a D h ɵ1ɵ1 ɵ2ɵ2 ADC is similar to CDB so ɵ 1 is also the upper angle in CDB, where tan ɵ 1 = a/h And m 2 = tan ɵ 2 = -h/a. Hence m 1 m 2 = (a/h)(-h/a) = -1.

8. Equations of Lines Vertical Lines, x = a Horizontal Lines, y = b Point-slope Form y – y 1 = m(x – x 1 ) Slope-Intercept Form, y = mx + b General Linear Equation (Standard Form), Ax + By = C

9. Write the equation of the line with the given information in point-slope form 1. (2, 3) and slope -3/2 2. (-2, -1) and (3, 4)

10. Write an equation for the line with the given information in slope- intercept form 1.Through (-1, 2) so its parallel to y=3x – 4 2. Repeat for perpendicular line

11. Use Standard Form to answer the following questions If 8x + 5y = 20 find the slope and y- intercept

12. Application Example #1 Find relationship between Fahrenheit and Celsius temperature. Then find the Celsius equivalent of 90 0 F and the Fahrenheit equivalent of -5 0 C.  F = mC + b  Freezing point for water is 32 0 F and 0 0 C, while boiling point of water is 212 0 F and 100 0 C.

13. Application Example #2 Regression Analysis: Build a linear model for the growth of the world population and then use the model to predict the world population in 2015.  Keep all decimals, rounding can seriously alter your data!!! YearPopulation in Millions 19864936 19875023 19885111 19895201 19905329 19915422

14. Steps for Regression Analysis 1. Plot Data (scatter plot) 2. Find regression equation in y = mx+b 3. Superimpose the graph of equation on scatter plot 4. Use equation to predict y-values for particular x-values

15. Homework Pages 7-9/ 3-45 multiples of 3, 49, & 51