Horizontal and Vertical Lines. 1. Consider the equation, y 5 26, that you wrote for the table shown in the previous activity.

Transcription

1 ACTIVITY 5. Horizontal and Vertical Lines Horizontal and vertical lines represent linear relationships, but their equations are different from the equations of lines that are not horizontal or vertical Consider the equation, 5 6, that ou wrote for the table shown in the previous activit. a. How is this equation different from the other equations? What is its slope? What is the -intercept? b. Describe the graph of the coordinate pairs in this table. Wh does the value of its slope make sense? c. Eplain wh the equation makes sense in terms of the graph and the table.. Write an equation for each linear relationship. Describe the graph of the linear relationship. State the slope and -intercept. a b. A line that passes through (15, 3.75) and (9, 3.75) M-1 TOPIC : Linear Relationships

2 3. Consider a new table of values representing a linear relationship. a. Eplain how this table is similar to and different from the tables in Questions 1 and. b. Write an equation for the linear relationship in the table c. Describe the graph of this linear relationship. d. Use the slope formula to calculate the slope between two points in the table. What do ou notice? 5 3 Theequation doesnothavean 6 Scope e. What is the -intercept of this linear relationship? Eplain wh this makes sense. FaasBesistinegistasiigtaatting. Write an equation for each linear relationship. Describe the graph of the linear relationship. a b. A line that passes through (7, 973) and (7, 5) Equation sasisalwase c. Create an additional table of values and write the equation for a vertical line. In a horizontal line there is no change in the -values as the -values change. Therefore, the slope is. A horizontal line has zero steepness. In a vertical line there is no change in the -values as the -values change. Therefore, the slope is undefined. A vertical line has an undefined steepness c a horizontal line g It horizontal line passesthrough ais at co crosses ais at 3.75J LESSON 5: What s the Point? M-11

3 Getting Started Draining the Pool X values are all Crus and Ava are pool cleaners who have been hired to drain the communit diving pools at the end of the summer. The are comparing the rate at which the two pools drain. X 1. For each pool, write an equation to represent the linear relationship. vertical line crosses ais a. Citscape Diving Pool is at a water level of 1 feet and drains at a rate of 3 feet per hour. UNDEFINED hdemnomainoatoirs z Xi Yi Yz C Slopeis undefined m C,5 C,1 I wonder if there is a wa to make writing the equation of a line more efficient. No intercept vertical line doesn'tcross ais b. Baside Diving Pool is at a water level of 15 feet after draining for hours and at 1 feet after draining for hours. I X 7. Compare our process for writing each equation. How are the processes different? A M-136 TOPIC : Linear Relationships sings.eq fs X slope undefined crosses ais

4 NOTES TALK the TALK Sa What? You have learned about two forms of a linear equation: the slope-intercept form, = m 1 b, and the point-slope form, 1 = m( 1 ). 1. What information can ou determine about each line b looking at the structure of the equation? a. = 3 5 b. 6 5 ( 1 1) c. 1 = d. 5 7 e. 1 5 = ( ) f Create a contet that represents a linear relationship that passes through the point (, 56) and has an increasing slope. Then write the equation of the line in point-slope form and slope-intercept form. M-1 TOPIC : Linear Relationships

5 A Elevation (feet) B Michele read the first pages of a mster novel before she fell asleep. The net da, she read one page ever two minutes until she finished the book, which was a total of 35 pages Time (seconds) 3 36 C D Number of Miles Time (hours) Water Level (feet) Number of Hours 9 E F Number of Games Ron Won Toda Number of Credits on Ron s Plaer s Card Bella s Pizza Shop charges $.5 for a small pizza, $7. for a medium pizza, and $9. for a large pizza. Additional toppings cost etra depending on the size of the pizza ordered. Bruce ordered a large pizza with three toppings that cost a total of $1.6. LESSON 5: What s the Point? M-15

6 Assignment Write Compare the slope-intercept and point-slope forms of a linear equation. Remember The point-slope form of a linear equation is 1 5 m( 1 ), where m is the slope of the line and ( 1, 1 ) is a point on the line. The slope of a horizontal line is. The slope of a vertical line is undefined. Practice Write an equation in point-slope form. 1. m 5 ; (5, 6). m 5 9.; (17, 1) 3. (, 3) and (, ). (79, 5) and (7, 55) 5. A photograph studio charges $5 for a sitting fee and 6 prints. Luigi increased his order to 11 prints and paid $ Zellie is taking the stairs in her building from her floor to the top of the building. After minutes, she was 1 steps from the bottom floor. After 5 minutes, she was 196 steps from the bottom floor. Write an equation in an form. 7. A newspaper charges a flat fee plus a charge per da to place a classified ad. Number of Das Total Charge ($) (, 1) (, ) LESSON 5: What s the Point? M-19

7 11. Pedro is traveling on a toll road. He plans to eit the road 5 miles ahead at First Avenue and pa $1.75. He changes his plans and travels 9 miles to Butler Street and pas $ Stretch To convert an equation from point-slope to slope-intercept form, ou can solve the equation for. How do ou convert from slope-intercept to point-slope form? Rewrite each equation in point-slope form using onl algebraic properties. What is special about the ordered pair now visible in the equation? Review 1. Write an equation in slope-intercept form with the given characteristics. a. The line is increasing and passes through the point (, 1). The slope of the line is less steep than the slope of the line represented b the equation 5 1. b. The line is decreasing and passes through the point (, 5). The slope of the line is more steep than the slope of the line represented b the equation For the linear equation 5 5, complete each task. a. Use a table of values to graph the linear equation. b. Use the points on the graph to sketch similar triangles that ma be used to show that the slope of a non-vertical line is the same between an two points on the line. c. Verif that the slopes are the same. 3. Solve each problem. a. What is a 15% tip for a restaurant bill of $? b. A $5 item was marked up %. What is the total increased cost of the item? M-15 TOPIC : Linear Relationships