X & Y Intercepts

1. X & Y Intercepts

2. Objectives • To learn what intercepts are • To learn how to find x and y-intercepts of a graph • To learn how to find x and y-intercepts of an equation • To use x and y-intercepts to sketch a graph

3. What does it mean to INTERCEPT a pass in football? The path of the defender crosses the path of the thrown football. In algebra, what are x- and y-intercepts?

4. What are x & y intercepts? • An intercept is where something intersects or touches • For example, • an x-intercept is where it touches the x-axis • a y-intercept is where it touches the y-axis

5. Intercepts of a Graph y • What are the x-intercept and y-intercept of the graph at right? • X-intercept: • Y-intercept: (0, 7) x (5, 0) (5, 0) (0, 7) Where it touches the y-axis Where it touches the x-axis

6. Intercepts of a Graph y • What are the x-intercept and y-intercept of the graph at right? • X-intercept: • Y-intercept: (0, 6) x (-8, 0) (-8, 0) (0, 6) Where it touches the y-axis Where it touches the x-axis

7. Intercepts of a Graph Notice: For all the x-intercepts the y-coordinate is ____ For all the y-intercepts the x-coordinate is ____ • What are the x and y-intercepts of the graphs below? 0 0 (-9, 0) X-intercept: (3, 0) X-intercept: (0, -5) Y-intercept: (0, -8) Y-intercept:

8. Intercepts of an Equation • We know for an x-intercept the ______________ is 0 • In the y-intercept the ___________ is 0 • We can use this to solve equations. • To solve for an x-intercept plug in a 0 for y. • To solve for a y-intercept plug in a 0 for x. Y-coordinate x-coordinate

9. y 5 x -5 -5 5 Hint: Cover up the 4y first. Cover up method Hint: Cover up the 2x this time. Solve for xandy. 2x + 4y= 8 2x + 4y = 8 2x = 8 4y = 8 x = 4 y = 2

10. y 5 x -5 -5 5 Finding X intercepts x + y = 5 x + (0) = 5 x = 5 (5, 0) x = 5

11. y 5 x -5 -3 7 Finding X intercepts 6x + 12y = 36 6x + 12(0) = 36 6x = 36 (6, 0) 6 6 x = 6

12. y 5 x -5 -5 5 Finding Y intercepts y = -3x - 4 y = -3(0) - 4 y = -4 y = -4 (0, -4)

13. y 7 x -3 -5 5 Finding Y intercepts y = ½ x + 6 (0, 6) y = ½ (0) + 6 y = 6 y = 6

14. y 5 x -5 -5 5 Use the Cover Up Method Solve for -6x – 4y = 2 -6x – 4y = 2 -6x = 2 x = -1/3 6x – 4y = 2 -4y = 2 y = -1/2

15. Introduction To Slope

16. Slope is a measure of steepness.

17. What is the meaning of this sign? • Icy Road Ahead • Steep Road Ahead • Curvy Road Ahead • Trucks Entering Highway Ahead

18. If a line goes upfrom left to right, then the slope is positive If a line goes down from left to right, then the slope is negative

19. Horizontal lines have a slope of zerowhile vertical lines have no slope = undefined slope = 0 no slope

20. Review… Zero Negative Positive Undefined or No Slope

21. Graph (3,2) and (-1,-1)

22. Draw a line through the points.

23. Now that we have our line lets find its slope. We are finding the following ratio: Vertical or Rise Horizontal Run

24. Vertical Changeor the Rise 3

25. Horizontal Changeor the Run 4 3

26. Vertical RiseHorizontal Run 3 4 Slope =

27. Find the slope of the following line. The slope is… If the line goes up the slope is positive. • 1 • 2

28. Find the slope of the line. The slope is…. If the line goes down the slope is negative. -3

29. Practice: Worksheet