5-2 Using Intercepts. Warm Up. Solve each equation. 1. 5x + 0 = = 0 + 3y. 4. 2x + 14 = 3x y 1 = 7y + 5

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1 Warm Up Solve each equation. 1. 5x + 0 = = 0 + 3y x + 14 = 3x y 1 = 7y + 5

2 Learning Goals 1. The student is able to find x and y-intercepts 2. The student is able to identify meanings of x and y-intercepts. 3. The student is able to use x and y-intercepts to graph an equation

3 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.

4 Example 1: Finding Intercepts Find the x- and y-intercepts. Then write them as ordered pairs A. B. C. The y-intercept is The y-intercept is The y-intercept is The x-intercept is (, ) (, ) The x-intercept is (, ) (, ) The x-intercept is (, ) (, )

5 Example 1: Finding Intercepts Find the x- and y-intercepts. Then write them as ordered pairs a. b. c. The y-intercept is The y-intercept is The y-intercept is The x-intercept is The x-intercept is The x-intercept is (, ) (, ) (, ) (, ) (, ) (, )

6 Example 1B: Finding Intercepts Find the x- and y-intercepts. A. 5x 2y = 10 To find the x-intercept, replace y with 0 and solve for x. To find the y-intercept, replace x with 0 and solve for y.

7 Example 1B: Finding Intercepts Find the x- and y-intercepts. A. 5x 2y = 10

8 Find the x- and y-intercepts. B. 3x + 5y = 30 To find the x-intercept, replace y with 0 and solve for x. To find the y-intercept, replace x with 0 and solve for y.

9 Find the x- and y-intercepts. B. 3x + 5y = 30

10 Find the x- and y-intercepts. a. 4x + 2y = 16 b. 3x - 2y = 12

11 Find the x- and y-intercepts. a. 4x + 2y = 16 To find the x-intercept, replace y with 0 and solve for x. To find the y-intercept, replace x with 0 and solve for y.

12 Find the x- and y-intercepts. b. 3x - 2y = 12 To find the x-intercept, replace y with 0 and solve for x. To find the y-intercept, replace x with 0 and solve for y.

13 The y-intercept represents 5-2 Using Intercepts Example 2: Sports Application A. Trish can run the 200 m dash in 25 s. The function f(x) = 200 8x gives the distance remaining to be run after x seconds. Graph this function and find the intercepts. What does each intercept represent? x f(x) = 200 8x The x-intercept represents

14 The y-intercept represents 5-2 Using Intercepts a. The school 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. x 2x + 3y =60 The x-intercept represents

15 b. 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)= x gives the tram s distance in meters from the top of the peak after x minutes. x f(x)= x The x-intercept represents The y-intercept represents

16 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. Helpful Hint You can use a third point to check your line. Either choose a point from your graph and check it in the equation, or use the equation to generate a point and check that it is on your graph.

17 Example 3A: Graphing Linear Equations by Using Intercepts Use intercepts to graph the line described by the equation. A. 3x 7y = 21 x-intercept: y-intercept:

18 Example 3A: Graphing Linear Equations by Using Intercepts Use intercepts to graph the line described by the equation. B. y = x + 4 x-intercept: y-intercept:

19 Example 3A: Graphing Linear Equations by Using Intercepts Use intercepts to graph the line described by the equation. C. 3x + 4y = 12 x-intercept: y-intercept:

20 Example 3A: Graphing Linear Equations by Using Intercepts Use intercepts to graph the line described by the equation. a. 2x - 4y = 8 x-intercept: y-intercept:

21 Example 3A: Graphing Linear Equations by Using Intercepts Use intercepts to graph the line described by the equation. b. y = 1 3 x 2 x-intercept: y-intercept:

22 Example 3A: Graphing Linear Equations by Using Intercepts Use intercepts to graph the line described by the equation. c. 5x - 10y = 20 x-intercept: y-intercept:

23 Lesson Quiz: Part I 1. An amateur filmmaker has $6000 to make a film that costs $75/h to produce. The function f(x) = x gives the amount of money left to make the film after x hours of production. Graph this function and find the intercepts. What does each intercept represent?

24 Lesson Quiz: Part II 2. Use intercepts to graph the line described by