1. NOTE: To change the image on this slide, select the picture and delete it. Then click the Pictures icon in the placeholder to insert your own image. FINDING SLOPE FROM TWO POINTS Lesson four

2. WARM UP 1.Find the slope of the line. Use rise over run. 2.Find the slope of the line. Use the slope formula. Show all your work. 3.You and your partner will complete the worksheet “Partner Problems” for a grade.

3. Vocabulary rate of change rise run slope Take a few minutes to write about each of the words above. What is a good definition for each?

4. In the coordinate plane, a line with positive slope rises from left to right. A line with negative slope falls from left to right. A line with 0 slope is horizontal. The slope of a vertical line is undefined.

5. If you know any two points on a line, you can find the slope of the line without graphing. The slope of a line through the points (x 1, y 1 ) and (x 2, y 2 ) is as follows: y2 – y1y2 – y1x2 – x1x2 – x1y2 – y1y2 – y1x2 – x1x2 – x1 When finding slope using the ratio above, it does not matter which point you choose for (x 1, y 1 ) and which point you choose for (x 2, y 2 ). slope =

6. The two points shown are: (0, -4) and (-3, -6). Now we have two points we can put them in the slope formula: Example #1

7. Example #2

8. Find the slope: (-3, 6) and (5, 2) Example #3

9. EQUATIONS OF HORIZONTAL AND VERTICAL LINES Equation of a Horizontal Line A horizontal line is given by an equation of the form y = b where b is the y-intercept. Note: m = 0. Equation of a Horizontal Line A horizontal line is given by an equation of the form y = b where b is the y-intercept. Note: m = 0. Equation of a Vertical Line A vertical line is given by an equation of the form x = a where a is the x-intercept. Note: m is undefined. Equation of a Vertical Line A vertical line is given by an equation of the form x = a where a is the x-intercept. Note: m is undefined.

10. Vertical Lines Now consider the vertical line of the equation x = 4 : A vertical line will have no slope, and “the slope is undefined" means that the line is vertical. The equation of all vertical lines are of the form x = “a number“ (ex. x = 4).

11. Horizontal Lines The points (-3, 4) and (5, 4), the slope is: For every horizontal line: a slope of zero means the line is horizontal, and a horizontal line means you'll get a slope of zero. The equation of all horizontals lines are of the form: y = “a number“ (ex. y = 4)

12. Find the slope using the pair of points below. 1)(-1, -6) and (2, 6) 2)(0, 1) and (3, 1) 3)(3, 5) and (3, 6) 4)(0, -7) and (4, 25) 5)(-1, 1) and (3, -3)

13. CLASSWORK You and your partner will complete a worksheet. One of you will complete all the even numbers and the other will complete all the odd numbers. You may help one another with the problems.

14. TICKET OUT THE DOOR…. Your friend is absent from school today. You will be going to visit your friend this afternoon after school. You intend to help him/her get caught up on today’s lesson. Write a few sentences explaining what was done in class today. Write down an example that you will use to explain the work to your friend.

15. HOMEWORK Tonight’s homework is from your workbook. Complete pages Show all your work!