MATH 90 CHAPTER 3 Name:.
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1 MATH 90 CHAPTER 3 Name:. 3.1 Reading Graphs & Plotting Points Need to Know Reading Graphs and Charts (Bar, Pie, Line) Plotting Points and Ordered Pairs and the Coordinate System Bar Graphs Data Source: U.S Census Bureau Kim plans to get an associate's degree. How much can she expect to make over her life time? Sam desires to make 3 million dollars in his life time. What level of education should he pursue? Pie Charts In 2005, the average American generated 4.5 lb of waste per day. How much of that was paper and cardboard? Scott Eckert pg. 1
2 The Coordinate System Vocabulary X-axis Y-axis Ordered Pair (x, y) Origin (0,0) Quadrants I, II, III, IV Graphing Ordered Pairs Ordered Pairs A B C D E Plot Each P is (-3, 4) Q is (0, 4) R is 7 2, 5 Line Graphs Make a line graph for the date in the table on a 10 x 10 grid. Year Tree Height (in.) Scott Eckert pg. 2
3 3.2 Graphing Linear Equations Need to Know Idea of solutions to linear equation in 2 variables Checking a solution to a linear equation in 2 variables How to find solutions to linear equation in 2 variables Linear Equations in 2 Variables Definition of a linear equation, is any equations that can be written in the form of where m, b, A, B and C are constants. It s graph is always a. Scott Eckert pg. 3
4 Checking a Solutions Are the points solutions to the equation 2x 3y = 12? (-3, -6) (8, -2) (6, 0) How to Find Solutions Find a solutions to 3x + y = 10 Think about the mental steps 1. (anything, either one doesn t matter) Graphing Linear Equations Graph the equation y = 2x 3 Scott Eckert pg. 4
5 Scott Eckert pg. 5
6 Application A smoker is 15 times more likely to die of lung cancer. An ex-smoker who stopped t years ago is w times more likely to die than a nonsmoker, where w = 15 t. Graph the equation. Sandy quit 2.5 years ago. Use the graph to predict Sandy s likelihood of dying from lung cancer compared to Sue who never smoked. end Intercepts Define and Find Intercepts The x-intercept point is the point where the line crosses the x-axis. The y-intercept point is the point where the line crosses the y-axis. How do you find them? Plug in zero for x and zero for y. Find the intercepts for: 3x 4y = -12 Scott Eckert pg. 6
7 Practice Graphing w/ Intercepts Find the intercepts and graph 2x y = -6 Practice Graphing w/ Intercepts Find the intercepts and graph 1 y x 4 Graphing Special Equations Graph the equation y = -2 X Y Scott Eckert pg. 7
8 Graphing Special Equations Graph the equation x = 4 X Y SUMMERIZE - Always Remember: x = number is a y = number is a 3.4 Rates Need To Know Understanding Rate of Change Visualizing Rate of Change Rate of Change Definition: A rate is a ratio that indicates how two quantities change with respect to each other. Examples: Find the rate - 1. The virus is growing 2000 cells in 15 minutes. 2. My car went 160 miles and used 7 gallon of gas. 3. Lauren took 18 hours to read 6 chapters. Scott Eckert pg. 8
9 Calculating Rates The company car you took on a business trip read 25,398 miles at the start and 25,719 miles at the end of the trip. You paid $41.60 for 13 gallons to fill the car back up. What is the rate of gas consumption in miles per gallon? Visualizing Rates In 2009, there were sales of $7 billion for a cancer drug. The sales are increasing at about 2.1 billion per year. 1) Label the axis 2) Select the scale 3) Plot some points Reading Rates from Graphs Use the graph to find the rate. At what rate does Eve cut hair? Scott Eckert pg. 9
10 3.5 The Slope of a Line Need to Know The idea of slope Slope characteristics 3 ways to find slope Scott Eckert pg. 10
11 The Idea of Slope We can measure slope by comparing vertical change to horizontal change. (x 1, y 1 ) (x 2, y 2 ) Slope = = ratio of change = = change in y. = change in x Practice 3 Ways to Find Slope Find Slope 1. From a picture rise run Find Slope of the lines. Practice 3 Ways to Find Slope Find Slope 1. From a picture rise run 2. From the points y 2 - y1 x - x From an equation Find Slope of the line through (-5,1) and (4,-6) Scott Eckert pg. 11
12 Practice 3 Ways to Find Slope Find Slope 1. From a picture rise run 2. From the points y 2 - y1 x - x From an equation Find Slope of the line through (-2,-3) and (4,-4) You try it! Practice 3 Ways to Find Slope Find Slope 1. From a picture rise run 2. From the points y 2 - y1 x - x From an equation Special Lines (Vertical or Horizontal) A) Find the slope of the line: y = -4 B) Find the slope of the line: x = The Equation of a Line Need To Know Graphing with a slope and intercept point Idea of the slope-intercept form of the equation of a line Working with parallel and perpendicular How to write equations of lines Scott Eckert pg. 12
13 Graphing Slope and Intercepts 1) Graph the line with the slope of 2/5 and a y-intercept of 4. 2) Graph the line with the slope of 3 and a y-intercept of -2. Equations of lines Graph and observe patterns y = 2x + 3 y = -1/3x + 3 y = x + 3 y = -4/5x + 3 y = Slope-Intercept Form for the Equation of a Line Slope-Intercept Form for the Equation of a Line m = of the line b = of the y-intercept point (0, b) is the Scott Eckert pg. 13
14 Graphing y = mx + b Find the slope and the y-intercept and graph 2 y x 4 3 3x + 2y = 12 Parallel and Perpendicular 1) Exit view mode 2) Select graphic 3) Grab green dot and rotate 90 4) Don t save a b l 1 a b l 2 a b l 1 If lines are parallel, then the slopes are Are these line parallel? y = -3x + 5 4y = 12x 8 If lines are perpendicular, then the slopes are Are these line perpendicular? y = -3x y = 4x 36 Finding an Equation for a Line To fiind an equation of a line you Find the equation of the line with a slope of 3 and a y-intercept through the point (0, 5). Need: 1. A slope 2. A point 3. A formula Find the equation of the line with a slope of 2/3 and a y-intercept through the point (0,-11). Scott Eckert pg. 14
15 Finding an Equation for a Line 1) Find the equation of the line that is parallel to the given line and has a y-intercept through the point (0, 5). Need: 1. A slope 2. A point 3. A formula 2) Write a slope-intercept equation of a line whose graph is perpendicular to y = -2x + 6 and has a y-intercept of (0, -3). end 3.7 Point-Slope Form Need To Know Idea of the point-slope form of the equation of a line How to write equations of lines Graphing with a point and a slope Writing an Equation for a Line y = mx + b is not always the best way to write an equation for a line. Write the equation of the line through the points (-4, 1) and (2, 3). To Write Line Equations Need: 1. A 2. A 3. A Scott Eckert pg. 15
16 Point-Slope Form for the Equation of a Line Point-Slope Form for the Equation of a Line The equation of a line through (x 1, y 1 ) with slope m is given by Scott Eckert pg. 16
17 Practice Write the equation of the line below in slope-intercept form. Need: 1. A slope 2. A point 3. A formula: Scott Eckert pg. 17
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