1. Introduction In this lesson, different methods will be used to graph lines and analyze the features of the graph. In a linear function, the graph is a straight line with a constant slope. All linear functions have a y-intercept. The y-intercept is where the graph crosses the y-axis. If a linear equation has a slope other than 0, then the function also has an x-intercept. The x-intercept is where the function crosses the x-axis. 1 3.4.1: Graphing Linear Functions

2. Key Concepts To find the y-intercept in function notation, evaluate f(0). The y-intercept has the coordinates (0, f(0)). To locate the y-intercept of a graphed function, determine the coordinates of the function where the line crosses the y-axis. 2 3.4.1: Graphing Linear Functions

3. Key Concepts, continued To find the x-intercept in function notation, set f(x) = 0 and solve for x. The x-intercept has the coordinates (x, 0). To locate the x-intercept of a graphed function, determine the coordinates of the line where the line crosses the x-axis. 3 3.4.1: Graphing Linear Functions

4. Key Concepts, continued To find the slope of a linear function, pick two coordinates on the line and substitute the points into the equation, where m is the slope, y 2 is the y-coordinate of the second point, y 1 is the y-coordinate of the first point, x 2 is the x-coordinate of the second point, and x 1 is the x-coordinate of the first point. If the line is in slope-intercept form, the slope is the x coefficient. 4 3.4.1: Graphing Linear Functions

5. Key Concepts, continued Graphing Equations Using a TI-83/84: Step 1: Press [Y=]. Step 2: Key in the equation using [X, T, , n] for x. Step 3: Press [WINDOW] to change the viewing window, if necessary. Step 4: Enter in appropriate values for Xmin, Xmax, Xscl, Ymin, Ymax, and Yscl, using the arrow keys to navigate. Step 5: Press [GRAPH]. 5 3.4.1: Graphing Linear Functions

6. Key Concepts, continued Graphing Equations Using a TI-Nspire: Step 1: Press the home key. Step 2: Arrow over to the graphing icon (the picture of the parabola or the U-shaped curve) and press [enter]. Step 3: Enter in the equation and press [enter]. Step 4: To change the viewing window: press [menu], arrow down to number 4: Window/Zoom, and click the center button of the navigation pad. 6 3.4.1: Graphing Linear Functions

7. Key Concepts, continued Step 5: Choose 1: Window settings by pressing the center button. Step 6: Enter in the appropriate XMin, XMax, YMin, and YMax fields. Step 7: Leave the XScale and YScale set to auto. Step 8: Use [tab] to navigate among the fields. Step 9: Press [tab] to “OK” when done and press [enter]. 7 3.4.1: Graphing Linear Functions

8. Common Errors/Misconceptions incorrectly plotting points mistaking the y-intercept for the x-intercept and vice versa being unable to identify key features of a linear model confusing the value of a function for its corresponding x-coordinate 8 3.4.1: Graphing Linear Functions

9. Guided Practice Example 2 Given the function, use the slope and y-intercept to identify the x-intercept of the function. 9 3.4.1: Graphing Linear Functions

10. Guided Practice: Example 2, continued 1.Identify the slope and y-intercept. The function is written in f(x) = mx + b form, where m is the slope and b is the y-intercept. The slope of the function is. The y-intercept is 2. 10 3.4.1: Graphing Linear Functions

11. Guided Practice: Example 2, continued 2.Graph the function on a coordinate plane. Use the y-intercept, (0, 2), and slope to graph the function. Be sure to extend the line to cross both the x- and y-axes. 11 3.4.1: Graphing Linear Functions

12. Guided Practice: Example 2, continued 3.Identify the x-intercept. The x-intercept is where the line crosses the x-axis. The x-intercept is (10, 0). 12 3.4.1: Graphing Linear Functions ✔

13. 13 3.4.1: Graphing Linear Functions Guided Practice: Example 2, continued 13

14. Guided Practice Example 3 Given the function, solve for the x- and y-intercepts. Use the intercepts to graph the function. 14 3.4.1: Graphing Linear Functions

15. Guided Practice: Example 3, continued 1.Find the x-intercept. Substitute 0 for f(x) in the equation and solve for x. Original function Substitute 0 for f(x). Subtract 4 from both sides. x = 3Divide both sides by. The x-intercept is (3, 0). 15 3.4.1: Graphing Linear Functions

16. Guided Practice: Example 3, continued 2.Find the y-intercept. Substitute 0 for x in the equation and solve for f(x). Original function Substitute 0 for x. Simplify as needed. f(x) = 4 The y-intercept is (0, 4). 16 3.4.1: Graphing Linear Functions

17. Guided Practice: Example 3, continued 3.Graph the function. Plot the x- and y-intercepts. 17 3.4.1: Graphing Linear Functions

18. Guided Practice: Example 3, continued Draw a line connecting the two points. 18 3.4.1: Graphing Linear Functions ✔

19. 19 3.4.1: Graphing Linear Functions Guided Practice: Example 3, continued