RECTANGULAR COORDINATE SYSTEM Section 3.2 YouTube Video Section 3.1. Plot (3,2), (4,0), (5,0), (-5,0) (0,6) (-3,2), (-4,0), (0,1), (1,0) (-7,-6)

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1 RECTANGULAR COORDINATE SYSTEM Section 3.2 YouTube Video Section 3.1 Plot (3,2), (4,0), (5,0), (-5,0) (0,6) (-3,2), (-4,0), (0,1), (1,0) (-7,-6) 1

2 Finding Solutions to a linear equation YouTube Video Is (3,4) a solutions to the equation x + y = 7? Complete the ordered pairs so that they are solutions of the equation x y 10 x y x y x y 2

3 Graphing linear equation YouTube Video The coordinates that make the following equations true are called solutions to the equation. x y 10 x y x y x y y 3 x 5 x y x y 3

4 YouTube Video X- and Y- intercepts x 5y 20 X-intercept Y-intercept 4 Let y=0 Let x=0 x 2y 2 X-intercept Y-intercept Let y=0 Let x=0 3 2y 15 x X-intercept Y-intercept Let y=0 Let x=0 1 x 3 2 y X-intercept Y-intercept Let y=0 Let x=0 4

5 Section 3.2 YouTube Video m=slope = = = m= m= m= m= 1. a) Graph the points (4,2) and (-3,0) b) Find the slope using the formula Find the slope by counting. 2. Find the Slope of the line a) b) y x y x

6 YouTube Video Find the slope and y-intercept for the following y=mx+b Section 3.3 Graph the following and label 2 points a) y x 3 2 b) y 2x c) 2x 3y 6. 6

7 Writing an equation of a line y mx b Section 3.4 1st find the slope 2nd find the y-intercept YouTube Video 1. Given a point (3,4) on the line and a slope of -3. Find the equation of the line. Or Try: Given a point (-1,5) on the line and a slope of 2. Find the equation of the line. 2. Given two points on the line (3,2) and (4,3). Find the equation of the line. Or Try: Given two points on the line (-1, 5) and (2,-4). Find the equation of the line. 7

8 Linear Applications Part I - Slope and y-intercept YouTube Video 1. The number of hot dogs I have eaten after a given number of days, t, is given by the formula A 5t 10 5 A t a) How many hot dogs have I eaten after 40 days. c) Slope =. Verbally interpret. Verbally interpret this result. b) When will the amount equal 300? d) y-intercept. = (, ) Verbally interpret. 2. The average price of a movie ticket is P 0.16t 4. 3, where t is the number of years since P t a) What is the price of a ticket price in c) Slope =. Verbally interpret. Verbally interpret. b) When was the movie ticket price $6.70? d) y-intercept. = (, ) Verbally interpret. 8

9 3. The cost of renting a truck for one day (in dollars) is C 0.3m 35, where m is the number of miles driven. C 0.3 m 1 35 a) What is the cost of renting a truck for the day after driving it 312 miles. Verbally interpret. b) How far can someone drive the truck during a one day rental if they have $80 to spend? c) Slope =. Verbally interpret. d) y-intercept. = (, ) Verbally interpret. 9

10 Linear Applications Part II - Slope and y-intercept YouTube Video Jimmy The Hands Bowman charges customer $5 monthly plus $1 per minute for backrubs. If you have $100 to spend monthly, then how many minutes can you afford? a) Form a linear equation: b) Answer the question. Matt s door service charges customer $100 monthly plus 30 per hour. If you have $1000 to spend monthly, then how many hours can you afford? a) Form a linear equation: b) Answer the question. Pooh s pick-up service charges $5 plus $2 a minute to remove your dogs excrement. Tigger s pick-up service charges a flat fee of $20. How many minutes would it take for Pooh s service to exceed the price of Tigger s? a) Form a linear equation: b) Answer the question. The Denver airport is 5200 ft above sea level. If a plane climbs at a constant rate of 1100 ft/min, then how long will it take the plane to reach 30,000 ft? a) Form a linear equation: b) Answer the question. 10

11 Linear Applications Part III - Slope and y-intercept YouTube Video Remember how to find the equation of the line 1) slope and a point, or 2) two points 1. The record for the 1500 meter run was 3.85 min in Twenty years later, the record stood at 3.70 min. a) Find a linear equation that models the data. b) Use that line to predict the number the record in c) If that trend continues, when will the record be 3.10 min? d) Slope =. Verbally interpret. e) y-intercept. = (, ) Verbally interpret. 11

12 6. After four months of use, Biffs Spiffy Spam-Free computer had dropped to $1100 in value. After ten months, the value had declined to $620. a) Find a linear equation that models the data. b) Slope =. Verbally interpret. c) y-intercept. = (, ) Verbally interpret. d) What was the original cost of the computer? e) How long will it take the computer s value to drop to $100? 12

13 Section 3.5 Slopes of Perpendicular and Parallel Lines YouTube Videos 1. a) If your line is parallel to a line with a slope of 3 then what is the slope of your line? b) If your line is perpendicular to a line with a slope of 3 then what is the slope of your line? c) If your line is perpendicular to a line with a slope of -1/2 then what is the slope of your line? 2. Find the slope of the line parallel to y - 3x = 4 3. Find the slope of the line perpendicular to y - 3x = 4 Find the slope of a line parallel and then a line that is perpendicular to the given line. Our line: Parallel line: Perpendicular line: 13

14 Finding the equation of the line (parallel and perpendicular) YouTube Video y mx b 1st find the slope 2nd find the y-intercept 1. Write the equation of a line parallel to y = 2x + 2. y = x + 3 Write the equation of a line perpendicular to y = 3x + 4. y = x Given a point (-2,0) and the line is perpendicular to y - 4x = Given a point (-2,3) and the line is parallel to 2y - 3x = Given a point (-2,0) and the line is perpendicular to y = 3. 14

15 FUNCTIONS YouTube Video Section 3.6 Ordered pair Relation Function Determine if the following are functions: 2,3, 4, 1, 5,3 1,0, 2, 1, 2,3 1,0, 2, 1, 3,3 f (x) means the value of the function f at x. Be careful f (x) doesn t mean f times x. 2 Let s start with a function f ( x) x 2x 4 f (1) f (3) f ( 5) f ( ) = f ( ) Write f(3) = 7 as an ordered pair: Write y = 2x + 1 as a function: y 2x 5 f ( x) 2x f ( 2) 2 x, y 2,1 15

16 Functions Part II YouTube Video f ( x) y y 2x 5 f ( x) 2x f ( 2) 2 x, y 2,1 1) Write y = 5x 4 as a function. 2) Given g ( x) 2x 4, Find: a) g(2) b) x when g(x) = 5 c) Fill in the blank (4, ) d) If g represents the number of gadgets in Jim's car after x days, then what is g(5) and what does it mean? f, and the domain of x is 2, 4, 5 2) If ( x) 5x 1, then what is the range of the function? 3) Average Trip Length The function since represents the average vehicle trip length T, in miles, x years a) Evaluate T(35). Provide a verbal explanation of the meaning of T(35). b) Evaluate T(0). Provide a verbal explanation of the meaning of T(0). 16

17 YouTube Video Domain: Range: Determine the domain and range for the following: 2,3, 4, 1, 5,3 1,0, 2, 1, 2,3 1,0, 2, 1, 3,3 Determine the domain and range and write the answer in interval notation: 17

18 Finding The Domain of a Function YouTube Video y 1 2 x 2 3x 5 y 3 x 1 y 2 x Try: x 2 y y x 3 x 2x 2 3x y x 1 y x 4 y 2x 3 2 x y x 2 Try: y 2x 3 y x 4 x 5 18

19 Graphing Linear Inequalities YouTube Video Find and plot some ordered pairs (x,y) that make the following inequalities true. Section 3.7 x y 10 y x 2, Dotted line, Solid line Graph: x 3 y 2x y 2x 3 2x 3y 6 19