1. CONFIDENTIAL 1 Algebra1 Using Intercepts

2. CONFIDENTIAL 2 Warm Up Solve each inequality and graph the solutions. 1) 3c > 12 2) -4 ≥ t 2 3) m ≥ -3 2 4) -2w > 14

3. CONFIDENTIAL 3 Using Intercepts A diver explored the ocean floor 120 feet below the surface and then ascended at a rate of 30 feet per minute. The graph shows the diver’s elevation below sea level during the ascent. 0 1 2 3 4 5 -45 -60 -15 -30 Elevation (ft) time (min) -105 -120 -75 -90 -135 The x-intercept is 4. It represents the time that the diver reaches the surface or when depth = 0. The y-intercept is -120. It represents the diver’s elevation at the start of the ascent when time = 0.

4. CONFIDENTIAL 4 The y-intercept is the y-coordinate of the point where the graph intersects the y-axis. The x-coordinate of this point is always 0. The x-intercept is the x-coordinate of the point where the graph intersects the x-axis. The y-coordinate of this point is always 0.

5. CONFIDENTIAL 5 Finding Intercepts 02-2-4 2 -2 -4 The graph intersects the y-axis at (0, -3). Find the x- and y-intercepts. A) The y-intercept is -3. The graph intersects the x-axis at (-4, 0). The x-intercept is -4. Next page 

6. CONFIDENTIAL 6 The x-intercept is 4. B) 3x - 2y = 12 To find the x-intercept, replace y with 0 and solve for x. 3x - 2y = 12 3x - 2 (0) = 12 3x - 0 = 12 3x = 12 3 3 x = 4 The y-intercept is -6. To find the y-intercept, replace x with 0 and solve for y. 3x - 2y = 12 3 (0) - 2y = 12 0 - 2y = 12 -2y = 12 -2 -2 y = -6

7. CONFIDENTIAL 7 Find the x- and y-intercepts. Now you try! 0 2 4 4 2 4 6 8 x 2 1) 2) -3x + 5y = 30

8. CONFIDENTIAL 8 Travel Application The Sandia Peak Tramway in Albuquerque, New Mexico, travels a distance of about 4500 meters to the top of Sandia Peak. Its speed is 300 meters per minute. The function f (x) = 4500 - 300x gives the tram’s distance in meters from the top of the peak after x minutes. Graph this function and find the intercepts. What does each intercept represent? Neither time nor distance can be negative, so choose several nonnegative values for x. Use the function to generate ordered pairs. x0251015 f(x) = 4500 - 300x45003900300015000 Next page 

9. CONFIDENTIAL 9 Graph the ordered pairs. Connect the points with a line. y-intercept: 4500. This is the starting distance from the top (time = 0). x-intercept: 15. This the time when the tram reaches the peak (distance = 0). Remember, to graph a linear function, you need to plot only two ordered pairs. It is often simplest to find the ordered pairs that contain the intercepts.

10. CONFIDENTIAL 10 Find the x- and y-intercepts. Now you try! 1.) The school store sells pens for $2.00 and notebooks for $3.00. The equation 2x + 3y = 60 describes the number of pens x and notebooks y that you can buy for $60. Graph the function and find its intercepts.

11. CONFIDENTIAL 11 Use intercepts to graph the line described by each equation. Graphing Linear Equations by Using Intercepts A) 2x - 4y = 8 Step1: Find the intercepts. The x-intercept is 4. x-intercept: 2x - 4y = 8 2x - 4 (0) = 8 2x = 8 2 x = 4 The y-intercept is -2. y-intercept: 2x - 4y = 8 2 (0) - 4y = 8 -4y = 8 -4 4 y = -2

12. CONFIDENTIAL 12 Step2: Graph the line. Plot (4, 0) and (0, -2). Connect with a straight line. 0 24 -4 2 4 -2 x (4, 0) (0, -2)

13. CONFIDENTIAL 13 B) y = 4 - x 2323 1212 2323 1212 6 y = 6 4 - x Multiply both sides by 6, the LCD of the fractions, to clear the fractions. 4y = 24 - 3x Write the equation in standard form. 3x + 4y = 24 Step1: Write the equation in standard form. Graphing Linear Equations by Using Intercepts

14. CONFIDENTIAL 14. x-intercept: y-intercept: The x-intercept is 8. 3x + 4y = 24 3x + 4 (0) = 24 3x = 24 3 3 x = 8 The y-intercept is 6. 3 (0) + 4y = 24 4y = 24 4 4 y = 6 3x + 4y = 24 Step2: Find the intercepts

15. CONFIDENTIAL 15 Step3: Graph the line. Plot (8, 0) and (0, 6). Connect with a straight line. 0 48 -8 4 8 12 16 x -4 (8, 0) (0, 6)

16. CONFIDENTIAL 16 Use intercepts to graph the line described by each equation. Now you try! 1) -3x + 4y = -12 1313 2) y = x - 2

17. CONFIDENTIAL 17 Assessment Find the x- and y-intercepts. 1)2)

18. CONFIDENTIAL 18 Find the x- and y-intercepts. 3) 4x + 2y = 164) 2x - 4y = 4 5) -2y = 3x - 66) 4y + 5x = 2y - 3x + 16

19. CONFIDENTIAL 19 7) To thaw a specimen stored at -25°C, the temperature of a refrigeration tank is raised 5°C every hour. The temperature in the tank after x hours can be described by the function f (x) = -25 + 5x. a. Graph the function and find its intercepts. b. What does each intercept represent?

20. CONFIDENTIAL 20 Use intercepts to graph the line described by each equation. 8) 2x + 3y = 6 9) 4x - 5y = 20 10) y = 2x + 4

21. CONFIDENTIAL 21 Using Intercepts A diver explored the ocean floor 120 feet below the surface and then ascended at a rate of 30 feet per minute. The graph shows the diver’s elevation below sea level during the ascent. 0 1 2 3 4 5 -45 -60 -15 -30 Elevation (ft) time (min) -105 -120 -75 -90 -135 The x-intercept is 4. It represents the time that the diver reaches the surface or when depth = 0. The y-intercept is -120. It represents the diver’s elevation at the start of the ascent when time = 0. Let’s review

22. CONFIDENTIAL 22 The y-intercept is the y-coordinate of the point where the graph intersects the y-axis. The x-coordinate of this point is always 0. The x-intercept is the x-coordinate of the point where the graph intersects the x-axis. The y-coordinate of this point is always 0.

23. CONFIDENTIAL 23 Finding Intercepts 02-2-4 2 -2 -4 The graph intersects the y-axis at (0, -3). Find the x- and y-intercepts. A) The y-intercept is -3. The graph intersects the x-axis at (-4, 0). The x-intercept is -4. Next page 

24. CONFIDENTIAL 24 The x-intercept is 4. B) 3x - 2y = 12 To find the x-intercept, replace y with 0 and solve for x. 3x - 2y = 12 3x - 2 (0) = 12 3x - 0 = 12 3x = 12 3 3 x = 4 The y-intercept is -6. To find the y-intercept, replace x with 0 and solve for y. 3x - 2y = 12 3 (0) - 2y = 12 0 - 2y = 12 -2y = 12 -2 -2 y = -6

25. CONFIDENTIAL 25 Travel Application The Sandia Peak Tramway in Albuquerque, New Mexico, travels a distance of about 4500 meters to the top of Sandia Peak. Its speed is 300 meters per minute. The function f (x) = 4500 - 300x gives the tram’s distance in meters from the top of the peak after x minutes. Graph this function and find the intercepts. What does each intercept represent? Neither time nor distance can be negative, so choose several nonnegative values for x. Use the function to generate ordered pairs. x0251015 f(x) = 4500 - 300x45003900300015000 Next page 

26. CONFIDENTIAL 26 Graph the ordered pairs. Connect the points with a line. y-intercept: 4500. This is the starting distance from the top (time = 0). x-intercept: 15. This the time when the tram reaches the peak (distance = 0). Remember, to graph a linear function, you need to plot only two ordered pairs. It is often simplest to find the ordered pairs that contain the intercepts.

27. CONFIDENTIAL 27 Use intercepts to graph the line described by each equation. Graphing Linear Equations by Using Intercepts A) 2x - 4y = 8 Step1: Find the intercepts. The x-intercept is 4. x-intercept: 2x - 4y = 8 2x - 4 (0) = 8 2x = 8 2 x = 4 The y-intercept is -2. y-intercept: 2x - 4y = 8 2 (0) - 4y = 8 -4y = 8 -4 4 y = -2

28. CONFIDENTIAL 28 Step2: Graph the line. Plot (4, 0) and (0, -2). Connect with a straight line. 0 24 -4 2 4 -2 x (4, 0) (0, -2)

29. CONFIDENTIAL 29 B) y = 4 - x 2323 1212 2323 1212 6 y = 6 4 - x Multiply both sides by 6, the LCD of the fractions, to clear the fractions. 4y = 24 - 3x Write the equation in standard form. 3x + 4y = 24 Step1: Write the equation in standard form. Graphing Linear Equations by Using Intercepts

30. CONFIDENTIAL 30. x-intercept: y-intercept: The x-intercept is 8. 3x + 4y = 24 3x + 4 (0) = 24 3x = 24 3 3 x = 8 The y-intercept is 6. 3 (0) + 4y = 24 4y = 24 4 4 y = 6 3x + 4y = 24 Step2: Find the intercepts

31. CONFIDENTIAL 31 Step3: Graph the line. Plot (8, 0) and (0, 6). Connect with a straight line. 0 48 -8 4 8 12 16 x -4 (8, 0) (0, 6)

32. CONFIDENTIAL 32 You did a great job today!