1. Bell Ringer Write down everything you know about creating graphs from equations. This is to be done individually.

2. Guided Practice Example #3 A gear on a machine turns at a rate of 2 revolutions per second. Let x represent time in seconds and let y represent number of revolutions. What is the equation that models the number of revolutions over time? 1.3.1: Creating and Graphing Linear Equations in Two Variables 2

3. Guided Practice: Example 3, continued 1.Read the problem and then reread the problem, determining the known quantities. What information are we given? 2 revolutions per second Label y axis # of revolutions Label x axis seconds 1.3.1: Creating and Graphing Linear Equations in Two Variables 3

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5. Guided Practice: Example 3, continued 4.Set up the coordinate plane. In this scenario, x represents the time passing after the gear began turning. The x-axis label is “Time in seconds.” The dependent variable, y, represents the number of revolutions of the gear. The y-axis label is “Revolutions.” 1.3.1: Creating and Graphing Linear Equations in Two Variables 5

6. Guided Practice: Example 3, continued 1.3.1: Creating and Graphing Linear Equations in Two Variables 6 Determine the scales to be used. The y-intercept is 0 and the slope is 2. The y-axis can be labeled in units of 1. If the slope was much larger we might consider changing the scale of the y-axis. Since the x-axis is in seconds, it makes sense that these units are in increments of 1. Since time cannot be negative, use only a positive scale for the x-axis.

7. Guided Practice: Example 3, continued 5.Graph the equation using the slope and y-intercept. Plot the y-intercept first. The y-intercept is 0. Remember that the y-intercept is where the graph crosses the y-axis and the value of x is 0. Therefore, the coordinate of the y-intercept will always have 0 for x. In this case, the coordinate of the y-intercept is (0, 0). 1.3.1: Creating and Graphing Linear Equations in Two Variables 7

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9. Guided Practice: Example 3, continued 1.3.1: Creating and Graphing Linear Equations in Two Variables 9 Place your pencil on the y-intercept. Move the pencil up 2 units, since the slope is positive. On this grid 2 units is 2 tick marks. Now, move your pencil to the right 1 unit for the run and plot a point. This is your second point. Repeat this process for a third point.

10. Guided Practice: Example 3, continued 7.Connect the points and extend the line. Then, label your line. Draw a line through the three points and add an arrow to the right end of the line to show that the line of the equation continues infinitely in that direction. Label the line with the equation, y = 2x. 1.3.1: Creating and Graphing Linear Equations in Two Variables 10

11. Guided Practice Example #5 A cab company charges an initial rate of $2.50 for a ride, plus $0.40 for each mile driven. What is the equation that models the total fee for using this cab company? 1.3.1: Creating and Graphing Linear Equations in Two Variables 11

12. Guided Practice: Example 5, continued 1.Read the problem and then reread the problem, determining the known quantities. What information are we given? $2.50 for a ride $0.40 for EACH mile Label y axis total fee Label x axis miles driven 1.3.1: Creating and Graphing Linear Equations in Two Variables 12

13. 1.3.1: Creating and Graphing Linear Equations in Two Variables 13

14. Guided Practice: Example 5, continued 4.Set up the coordinate plane. In this scenario, x represents the miles traveled after the ride starts. The x-axis label is “miles traveled.” The dependent variable, y, represents the total fee. The y-axis label is “total fee.” 1.3.1: Creating and Graphing Linear Equations in Two Variables 14

15. Guided Practice: Example 5, continued 1.3.1: Creating and Graphing Linear Equations in Two Variables 15 Determine the scales to be used. The y-intercept is 2.50 and the slope is.40. The y-axis can be labeled in units of 0.1. Since the x-axis is in miles, it makes sense that these units are in increments of 1. Since distance cannot be negative, use only a positive scale for the x-axis.

16. Guided Practice: Example 5, continued 5.Graph the equation using the slope and y-intercept. Plot the y-intercept first. The y-intercept is 2.50. Remember that the y- intercept is where the graph crosses the y-axis and the value of x is 0. Therefore, the coordinate of the y- intercept will always have 0 for x. In this case, the coordinate of the y-intercept is (0, 2.50). 1.3.1: Creating and Graphing Linear Equations in Two Variables 16

17. 1.3.1: Creating and Graphing Linear Equations in Two Variables 17

18. Guided Practice: Example 5, continued 1.3.1: Creating and Graphing Linear Equations in Two Variables 18 Place your pencil on the y-intercept. Move the pencil up 4 units, since the slope is positive. On this grid 4 units is 4 tick marks. Now, move your pencil to the right 1 unit for the run and plot a point. This is your second point. Repeat this process for a third point.

19. Guided Practice: Example 5, continued 7.Connect the points and extend the line. Then, label your line. Draw a line through the three points and add an arrow to the right end of the line to show that the line of the equation continues infinitely in that direction. Label the line with the equation, y =.4x+2.50. 1.3.1: Creating and Graphing Linear Equations in Two Variables 19