12-1 Graphing Linear Equations. Warm Up Problem of the Day Lesson Presentation. Course 3

Transcription

1 Warm Up Problem of the Day Lesson Presentation

2 Warm Up Solve each equation for y. 1. 6y 1x = 4. y 4x = 0 3. y 5x = y + 6x = 18 y = x + 4 y = x 10 y = 5 x + 8 y = x + 6

3 Problem of the Day The same photo book of Niagara Falls costs $5.95 in the United States and $8.5 in Canada. If the exchange rate is $1.49 in Canadian dollars for each U.S. dollar, in which country is the book a better deal? Canada

4 Learn to identify and graph linear equations.

5 1-1 Graphing Insert Lesson Linear Title Equations Here linear equation Vocabulary

6 A linear equation is an equation whose solutions fall on a line on the coordinate plane. All solutions of a particular linear equation fall on the line, and all the points on the line are solutions of the equation. To find a solution that lies between two points (x 1, y 1 ) and (x, y ), choose an x-value between x 1 and x and find the corresponding y-value.

7 1-1 Insert Graphing Lesson Linear Title Equations Here Reading Math Read x 1 as x sub one or x one.

8 If an equation is linear, a constant change in the x-value corresponds to a constant change in the y-value. The graph shows an example where each time the x-value increases by 3, the y-value increases by

9 Additional Example 1A: Graphing Equations Graph the equation and tell whether it is linear. y = 3x 1 x 3x 1 y (x, y) ( ) 1 3( 1) 1 3(0) 1 3(1) 1 3() (, 7) ( 1, 4) (0, 1) (1, ) (, 5)

10 Additional Example 1A Continued The equation y = 3x 1 is a linear equation because it is the graph of a straight line and each time x increases by 1 unit, y increases by 3 units.

11 1-1 Insert Graphing Lesson Linear Title Equations Here Caution! Be careful when graphing each ordered pair. Double check each point you plot.

12 Additional Example 1B: Graphing Equations Graph the equation and tell whether it is linear. y = x 3 x x 3 y (x, y) ( ) 3 ( 1) 3 (0) 3 (1) 3 () (, 8) ( 1, 1) (0, 0) (1, 1) (, 8)

13 Additional Example 1B Continued The equation y = x 3 is not a linear equation because its graph is not a straight line. Also notice that as x increases by a constant of 1 unit, the change in y is not constant. x y

14 Additional Example 1C: Graphing Equations Graph the equation and tell whether it is linear. y = 3x 4

15 Additional Example 1 Continued The equation y = is a linear equation because the points form a straight line. Each time the value of x increases by 1, the value of y decreases by or y decreases by 3 each time x increases by 4. 3x 4 3 4

16 Additional Example 1D: Graphing Equations Graph the equation and tell whether it is linear. y = x y (x, y) For any value of x, y =. (, ) ( 1, ) (0, ) (1, ) (, )

17 Additional Example 1D Continued The equation y = is a linear equation because the points form a straight line. As the value of x increases, the value of y has a constant change of 0.

18 Graph the equation and tell whether it is linear. y = x + 1 Check it Out: Example 1A x x + 1 y (x, y) ( 4) + 1 ( ) + 1 (0) + 1 () + 1 (4) ( 4, 7) (, 3) (0, 1) (, 5) (4, 9)

19 Check It Out: Example 1A Continued The equation y = x + 1 is linear equation because it is the graph of a straight line and each time x increase by 1 unit, y increases by units.

20 Graphing the equation and tell whether it is linear. y = x Check It Out: Example 1B x x y (x, y) ( ) 4 ( 1) 1 (0) (1) () (, 4) ( 1, 1) (0, 0) (1, 1) (, 4)

21 Check It Out: Example 1B Continued The equation y = x is not a linear equation because its graph is not a straight line.

22 Check It Out: Example 1C Graph the equation and tell whether it is linear. y = x x y (x, y) ( 8, 8) ( 6, 6) (0, 0) (4, 4) (8, 8)

23 Check It Out: Example 1C Continued The equation y = x is a linear equation because the points form a straight line. Each time the value of x increases by 1, the value of y increases by 1.

24 Check It Out: Example 1D Graph the equation and tell whether it is linear. D. y = 7 x 7 y (x, y) For any value of x, y = ( 8, 7) ( 4, 7) (0, 7) (4, 7) (8, 7)

25 Check It Out: Example 1D Continued The equation y = 7 is a linear equation because the points form a straight line. As the value of x increases, the value of y has a constant change of 0.

26 Additional Example : Sports Application A lift on a ski slope rises according to the equation a = 130t + 650, where a is the altitude in feet and t is the number of minutes that a skier has been on the lift. Five friends are on the lift. What is the altitude of each person if they have been on the ski lift for the times listed in the table? Draw a graph that represents the relationship between the time on the lift and the altitude.

27 Additional Example Continued

28 Additional Example Continued

29 Additional Example Continued The altitudes are: Anna, 6770 feet; Tracy, 6640 feet; Kwani, 6510 feet; Tony, 6445 feet; George, 6380 feet. This is a linear equation because when t increases by 1 unit, a increases by 130 units. Note that a skier with 0 time on the lift implies that the bottom of the lift is at an altitude of 650 feet.

30 Check It Out: Example In an amusement park ride, a car travels according to the equation D = 150t where t is time in minutes and D is the distance in feet the car travels. Below is a chart of the time that three people have been in the cars. Graph the relationship between time and distance. How far has each person traveled? Rider Ryan Greg Colette Time 1 min min 3 min

31 Check It Out: Example Continued t D =150t D (t, D) 1 150(1) 150 (1, 150) 150() 500 (, 500) 3 150(3) 3750 (3, 3750) The distances are: Ryan, 150 ft; Greg, 500 ft; and Collette, 3750 ft.

32 Distance (ft) 1-1 Graphing Linear Equations Check It Out: Example Continued y Time (min) x This is a linear equation because when t increases by 1 unit, D increases by 150 units.

33 1-1 Graphing Insert Lesson Linear Title Equations Here Lesson Quiz Graph each equation and tell whether it is linear. 1. y = 3x 1. y = 1 x 4 3. y = x 3 yes yes no