The Straight Line

1. The Straight Line

2. Change in vertical distance Change in horizontal distance rise run = Reminder: Gradient = You can start and end anywhere on the line.

3. What happens when the line slopes down? In this case the gradient is negative.

4. Reminder: Gradient Formula y Negative gradient 8 Positive gradient -2 1 6 4 2 x -5 5 10 -2 -4 What are the gradients of these two lines? Now check the gradients using the formula. (-3, 7) (3, 6) (0, 3) (-1, 3)

5. Gradient Exercise

6. Example: Sketch the line Reminder: Sketching Lines Given the equation of a line, we can sketch it by making a table and finding points which lie on the line. We usually find three points. We plot the points (0, -2) (2, 4) (4, 10)

7. Plot the points • Draw line through the points (4, 10) (2, 4) (0, -2)

8. 2 1 4 5 3 1 2 We will now look at more lines and their equations What do you notice? What is the gradient of each line? Where does each line cut the y axis?

9. - 2 - 6 + 1 Here are some more lines What do you notice? What is the gradient of each line? Where does each line cut the y axis?

10. m = 3 c = -2 So far all the lines we have looked have been of the form y= mx + c y-intercept gradient We will look at this more closely using Autograph

11. What do you think the gradient of the line is? Check this using the graph. Where do you think it cuts the y axis?

12. What about ? Again check this using the graph.

13. (a) (b) (c) (d) The equation of the line shown is

14. The graph of y = 3x + 1 is A B C D

15. Sorry that is incorrect! Try again.

16. Well Done! Click to continue.

17. Well Done! Click to continue.

18. No of Videos (N) 0 1 2 3 4 5 6 Cost of Videos(£) (C) Consider the following problem You join a video shop for a membership fee of £3 and then charge £2 for each video you hire. We can draw a graph of Cost against Number of Videos by making a table. 3 5 7 9 11 13 15 Now draw a graph of the table above.

19. Instead of x we have N. • Instead of y we have C. • What is the gradient of this line? • What is the y-intercept? What is the equation of this line? We can use y = mx + c to find a formula for the cost of hiring any number of videos. Were you correct? Answer:C = 2N + 3 What does the gradient of 2 tell us? For every square that you move to the right you go two squares up because the cost of each video is £2. What does the y-intercept tell us? You always have to pay £3.

20. Answer: Another problem: Find the equation of the line below. Method: • Write down the coordinates of 2 points on the line. • Use the gradient formula to find m. • Read off c. • Write down the equation in the form y = mx + c. • Write down the equation in terms of s and P.

21. Special Cases Lines parallel to the x and y axes. 1. Parallel to the x-axis Notice: the y coordinate of every point on this line is 3 Using the gradient formula with (0, 3) and (6, 3) gives Using y = mx + c We say the equation of the line is y = 3 Also c = 3

22. Special Cases Lines parallel to the x and y axes. 2. Parallel to the y-axis Using the gradient formula with (4, 2) and (4, 5) gives Notice: the x coordinate of every point on this line is 4 We say the equation of the line is x = 4 This is because you cannot divide by zero! This means you cannot use y = mx + c However……..