1 - 1 © 2012 Pearson Education, Inc.. All rights reserved. Section 1.1 Slopes and Equations of Lines How are linear relationships used to model and solve real world problems?

1 - 2 © 2012 Pearson Education, Inc.. All rights reserved. Match each term to a correct description. TermsDescriptions 1. point-slope formA. Where x- and y- axes cross. 2. Horizontal lineB. Graph with No slope 3. Vertical lineC. Slopes are the same 4. Perpendicular linesD. x-coordinate is negative and y-coordinate is negative 5. Parallel linesE nd QuadrantF. Has two axes and four quandrants 7. 3 rd QuadrantG. Slopes are opposite reciprocals 8. Cartesian Coordinate PlaneH. Graph has slope of zero 9. OriginI. x-coordinate is negative and y-coordinate is positive. How are linear relationships used to model and solve real world problems?

1 - 3 © 2012 Pearson Education, Inc.. All rights reserved. Quadrants How are linear relationships used to model and solve real world problems?

1 - 4 © 2012 Pearson Education, Inc.. All rights reserved. Intercepts & Slopes How are linear relationships used to model and solve real world problems?

1 - 5 © 2012 Pearson Education, Inc.. All rights reserved. How are linear relationships used to model and solve real world problems?

1 - 6 © 2012 Pearson Education, Inc.. All rights reserved. Possible Slopes of lines How are linear relationships used to model and solve real world problems?

1 - 7 © 2012 Pearson Education, Inc.. All rights reserved. Your Turn 1 – Check for Understanding Find the slope of the line through (1,5) and (4,6). How are linear relationships used to model and solve real world problems?

1 - 8 © 2012 Pearson Education, Inc.. All rights reserved. Writing Equations How are linear relationships used to model and solve real world problems?

1 - 9 © 2012 Pearson Education, Inc.. All rights reserved. Examples: Find an equation of a line who passes through the points (8,9) and (-2,3) How are linear relationships used to model and solve real world problems?

© 2012 Pearson Education, Inc.. All rights reserved. Figure 5 How are linear relationships used to model and solve real world problems?

© 2012 Pearson Education, Inc.. All rights reserved. Your Turn 2 – Check for Understanding Find the equation of the line with x-intercept − 4 and y-intercept 6. Solution: Notice that b = 6. To find m, use the definition of the slope after writing the x-intercept as (− 4, 0) and y-intercept as (0,6). Substituting these values into y = mx + b, we have How are linear relationships used to model and solve real world problems?

© 2012 Pearson Education, Inc.. All rights reserved. Your Turn 3 – Check for Understanding How are linear relationships used to model and solve real world problems?

© 2012 Pearson Education, Inc.. All rights reserved. Your Turn 4 – Check for Understanding How are linear relationships used to model and solve real world problems?

© 2012 Pearson Education, Inc.. All rights reserved. Assessment Prompt  Ones do Page 13 #1,7,11,15,19  Twos do Page 13 #3,5,9,17,21  Check each other’s work….Be prepared to defend your answers. How are linear relationships used to model and solve real world problems?

© 2012 Pearson Education, Inc.. All rights reserved. A Quick Review How are linear relationships used to model and solve real world problems?

© 2012 Pearson Education, Inc.. All rights reserved. Homework  Page 13 #2-12 even & #16-24 even How are linear relationships used to model and solve real world problems?

© 2012 Pearson Education, Inc.. All rights reserved. Parallel & Perpendicular lines How are linear relationships used to model and solve real world problems?

© 2012 Pearson Education, Inc.. All rights reserved. Your Turn 5 How are linear relationships used to model and solve real world problems?

© 2012 Pearson Education, Inc.. All rights reserved. Your Turn 5 continued How are linear relationships used to model and solve real world problems?

© 2012 Pearson Education, Inc.. All rights reserved. Your Turn 6 How are linear relationships used to model and solve real world problems?

© 2012 Pearson Education, Inc.. All rights reserved. Your Turn 6 continued How are linear relationships used to model and solve real world problems?

© 2012 Pearson Education, Inc.. All rights reserved. Assessment Prompt  Think-Pair-Share  Page 13 #13,14,29,31,33  Check each other’s work….Be prepared to defend your answers. How are linear relationships used to model and solve real world problems?

© 2012 Pearson Education, Inc.. All rights reserved. Applications The table on the left lists the average annual cost (in dollars) of tuition and fees at public four-year colleges for selected years. a) Plot the cost of public colleges by letting t = 0 correspond to Are the data exactly linear? b) Use the points (0,3508) and (9,7020) to determine an equation that models the data. c) How accurate is this equation in representing the cost of public colleges? Explain in context. How are linear relationships used to model and solve real world problems?

© 2012 Pearson Education, Inc.. All rights reserved. Graph of Tuition and Fees How are linear relationships used to model and solve real world problems?

© 2012 Pearson Education, Inc.. All rights reserved. Assessment Prompt  Think-Pair-Share  Page 16 #71  Check each other’s work….Be prepared to defend your answers. How are linear relationships used to model and solve real world problems?

© 2012 Pearson Education, Inc.. All rights reserved. Lesson Assignment  News/Talk Radio Math Modeling  Find a linear equation to model the number of stations carrying News/Talk Radio  Explain, in words, your process of finding this linear equation.  Predict the number of stations carrying news/talk radio in Compare this number with the actual amount.  Predict the number of stations carrying news/talk radio in How confidant can you be about your prediction? How are linear relationships used to model and solve real world problems?

© 2012 Pearson Education, Inc.. All rights reserved. Homework  Pages #26-38even, and #50,52,58,62,64,66,68 How are linear relationships used to model and solve real world problems? Exit Ticket: Why is slope important?