Download presentation

Presentation is loading. Please wait.

1
**The x- and y-Intercepts**

Topic 4.2.4

2
**The x- and y-Intercepts**

Topic 4.2.4 The x- and y-Intercepts California Standard: 6.0 Students graph a linear equation and compute the x- and y-intercepts (e.g. graph 2x + 6y = 4). They are also able to sketch the region defined by a linear inequality (e.g. they sketch the region defined by 2x + 6y < 4). What it means for you: You’ll learn about x- and y-intercepts and how to compute them from the equation of a line. Key Words: intercept linear equation

3
**The x- and y-Intercepts**

Topic 4.2.4 The x- and y-Intercepts –4 –2 2 4 y x The intercepts of a graph are the points where the graph crosses the axes. This Topic is all about how to calculate them.

4
**The x- and y-Intercepts**

Topic 4.2.4 The x- and y-Intercepts The x-Intercept is Where the Graph Crosses the x-Axis The x-axis on a graph is the horizontal line through the origin. Every point on it has a y-coordinate of 0. That means that all points on the x-axis are of the form (x, 0). The x-intercept of the graph of Ax + By = C is the point at which the graph of Ax + By = C crosses the x-axis. –4 –2 2 4 y-axis x-axis The x-intercept is here (–1, 0)

5
**The x- and y-Intercepts**

Topic 4.2.4 The x- and y-Intercepts Computing the x-Intercept Using “y = 0” Since you know that the x-intercept has a y-coordinate of 0, you can find the x-coordinate by letting y = 0 in the equation of the line. –4 –2 2 4 y-axis x-axis (–1, 0)

6
**The x- and y-Intercepts**

Topic 4.2.4 The x- and y-Intercepts Example 1 Find the x-intercept of the line 3x – 4y = 18. Solution Let y = 0, then solve for x: 3x – 4y = 18 3x – 4(0) = 18 3x – 0 = 18 3x = 18 x = 6 So (6, 0) is the x-intercept of 3x – 4y = 18. Solution follows…

7
**The x- and y-Intercepts**

Topic 4.2.4 The x- and y-Intercepts Example 2 Find the x-intercept of the line 2x + y = 6. Solution Let y = 0, then solve for x: 2x + y = 6 2x + 0 = 6 2x = 6 x = 3 So (3, 0) is the x-intercept of 2x + y = 6. Solution follows…

8
**The x- and y-Intercepts**

Topic 4.2.4 The x- and y-Intercepts Guided Practice In Exercises 1–8, find the x-intercept. 1. x + y = 5 2. 3x + y = 18 3. 5x – 2y = –10 4. 3x – 8y = –21 5. 4x – 9y = 16 6.15x – 8y = 5 7. 6x – 10y = –8 8. 14x – 6y = 0 x + 0 = 5 Þ x = 5 Þ (5, 0) 3x + 0 = 15 Þ x = 6 Þ (6, 0) 5x – 2(0) = –10 Þ x = –2 Þ (–2, 0) 3x – 8(0) = –21 Þ x = –7 Þ (–7, 0) 4x – 9(0) = 16 Þ x = 4 Þ (4, 0) 15x – 8(0) = 5 Þ x = Þ ( , 0) 1 3 6x – 10(0) = –8 Þ x = – Þ (– , 0) 4 3 14x – 6(0) = 0 Þ x = 0 Þ (0, 0) Solution follows…

9
**The x- and y-Intercepts**

Topic 4.2.4 The x- and y-Intercepts The y-Intercept is Where the Graph Crosses the y-Axis The y-axis on a graph is the vertical line through the origin. Every point on it has an x-coordinate of 0. That means that all points on the y-axis are of the form (0, y). The y-intercept of the graph of Ax + By = C is the point at which the graph of Ax + By = C crosses the y-axis. –4 –2 2 4 6 y-axis x-axis –0 The y-intercept here is (0, 3)

10
**The x- and y-Intercepts**

Topic 4.2.4 The x- and y-Intercepts Computing the y-Intercept Using “x = 0” Since the y-intercept has an x-coordinate of 0, find the y-coordinate by letting x = 0 in the equation of the line. –4 –2 2 4 6 y-axis x-axis –0 (0, 3)

11
**The x- and y-Intercepts**

Topic 4.2.4 The x- and y-Intercepts Example 3 Find the y-intercept of the line –2x – 3y = –9. Solution Let x = 0, then solve for y: –2x – 3y = –9 –2(0) – 3y = –9 0 – 3y = –9 –3y = –9 y = 3 So (0, 3) is the y-intercept of –2x – 3y = –9. Solution follows…

12
**The x- and y-Intercepts**

Topic 4.2.4 The x- and y-Intercepts Example 4 Find the y-intercept of the line 3x + 4y = 24. Solution Let x = 0, then solve for y: 3x + 4y = 24 3(0) + 4y = 24 0 + 4y = 24 4y = 24 y = 6 So (0, 6) is the y-intercept of 3x + 4y = 24. Solution follows…

13
**The x- and y-Intercepts**

Topic 4.2.4 The x- and y-Intercepts Guided Practice In Exercises 9–16, find the y-intercept. 9. 4x – 6y = 24 10. 5x + 8y = 24 11. 8x + 11y = –22 12. 9x + 4y = 48 13. 6x – 7y = –28 14. 10x – 12y = 6 15. 3x + 15y = –3 16. 14x – 5y = 0 4(0) – 6y = 24 Þ y = –4 Þ (0, –4) 5(0) + 8y = 24 Þ y = 3 Þ (0, 3) 8(0) + 11y = –22 Þ y = –2 Þ (0, –2) 9(0) + 4y = 48 Þ y = 12 Þ (0, 12) 6(0) – 7y = –28 Þ y = 4 Þ (0, 4) 10(0) – 12y = 6 Þ y = –0.5 Þ (0, –0.5) 3(0) + 15y = –3 Þ y = –0.2 Þ (0, –0.2) 14(0) – 5y = 0 Þ y = 0 Þ (0, 0) Solution follows…

14
**The x- and y-Intercepts**

Topic 4.2.4 The x- and y-Intercepts Independent Practice 1. Define the x-intercept. 2. Define the y-intercept. The point at which the graph of a line crosses the y-axis. The point at which the graph of a line crosses the x-axis. Solution follows…

15
**The x- and y-Intercepts**

Topic 4.2.4 The x- and y-Intercepts Independent Practice Find the x- and y-intercepts of the following lines: 3. x + y = x – y = 7 5. –x – 2y = x – 3y = 9 7. 3x – 4y = –2x + 3y = 12 9. –5x – 4y = –0.2x + 0.3y = 1 x – 0.2y = – x – y = 6 (9, 0); (0, 9) (7, 0); (0, –7) (–4, 0); (0, –2) (9, 0); (0, –3) (8, 0); (0, –6) (–6, 0); (0, 4) (–5, 0); (0, 3 ) 1 3 (–4, 0); (0, –5) 1 2 2 3 (–12, 0); (0, –9) (8, 0); (0, –10) Solution follows…

16
**The x- and y-Intercepts**

Topic 4.2.4 The x- and y-Intercepts Independent Practice 13. ( g, 0) is the x-intercept of the line –10x – 3y = 12. Find the value of g. 14. (0, k) is the y-intercept of the line 2x – 15y = –3. Find the value of k. 15. The point (–3, b) lies on the line 2y – x = 8. Find the value of b. 16. Find the x-intercept of the line in Exercise 15. 17. Another line has x-intercept (4, 0) and equation 2y + kx = 20. Find the value of k. 3 5 1 g = –2 k = 1 b = 2.5 (–8, 0) k = 5 Solution follows…

17
**The x- and y-Intercepts**

Topic 4.2.4 The x- and y-Intercepts Independent Practice In Exercises 18-22, use the graph below to help you reach your answer. 18. Find the x- and y-intercepts of line n. 19. Find the x-intercept of line p. 20. Find the y-intercept of line r. 21. Explain why line p does not have a y-intercept. 22. Explain why line r does not have an x-intercept. –6 –4 –2 2 4 6 y x p n r (1, 0); (0, –4) (–3, 0) (0, 2) Line p is vertical and never crosses the y-axis. Line r is horizontal and never crosses the x-axis. Solution follows…

18
**The x- and y-Intercepts**

Topic 4.2.4 The x- and y-Intercepts Round Up Make sure you get the method the right way around — to find the x-intercept, put y = 0 and solve for x, and to find the y-intercept, put x = 0 and solve for y. In the next Topic you’ll see that the intercepts are really useful when you’re graphing lines from the line equation.

Similar presentations

Presentation is loading. Please wait....

OK

Quizzes Pencil and calculators only..

Quizzes Pencil and calculators only..

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google