1. Why did the girl wear glasses during math class? Why was six afraid of seven?

2. What is slope? When is it used? How can it be found?

3. Finding slope Find the slope for the following Joy rides her bike 5 miles per hour. (0,0)(1,5) (2,6)(-3,5) Y=2x+7 Y=-3x +4 5/1 1/5 2 -3

4. Slope fomula (y 1 - y)/(x 1 - x ) Slope formula measures the rise divided by the run. Find the rise by subtracting y coordinates of 2 points on a line. Find the run by subtracting the x coordinates of 2 points on a line Example (3,8) (7,-1) Change in y 8 - -1 = 9 Change in x 3 – 7 = -4 9/-4 is the slope

5. Slope with formula and slope triangle Example (3,8) (7,-1) Change in y is 8 - -1 = 9 Change in x is 3 – 7 = -4 9/-4 is the slope

6. Determine if the following lines are translations Line a (2,3)(4,5) Line b (2, 4)(4,6) Y=2x+5 Y=2x +2

9. When would it be important to determine if two lines are parallel

10. Given two points on two lines determine if the lines are parallel. (0,0)(1,2) (0,3)(1,5) Are the slopes the same? Is one a translation of the other?

11. Given two points on two lines determine if the lines are parallel. (3,-1)(5,3) (-1,3)(1,6) Are the slopes the same? Is one a translation of the other?

12. Given two linear equations can you determine if they are parallel? Y=2/3x +4 Y= 2/3x +1 Are the slopes the same? Is one a translation of the other?

13. Parallel lines In 2008 the snowpack melted from the mountains at 7 inches per week The beginning snow pack was 100 inches. In 2010 The snowpack melted from the mountains at 7 inches per week. The beginning snow pack was 110 inches. Explain how the graphs of these two situations would compare to each other.

14. Perpendicular lines Perpendicular lines have slopes that are opposite reciprocals. Slope 2/3 Slope -3/2 Think of the two triangles as a 90 degree rotation.

15. Perpendicular lines Which of the following lines are perpendicular? Which of the following lines are parallel? Which of the following lines are neither? Line aLine b Problem 1Y=2x+4Y=-2x+3 Problem 2Y= -3x+1Y= -1/3x +2 Problem 3Y= 5x +3Y= -1/5x +1 Problem 4Y= 3/4x+2Y=3/4x -2 Problem 5Y= -2/3x +1Y=3/2x -1 Problem 62x+y = 8X- 2y =12

16. Perpendicular lines Are the two lines represented by the following points going to be perpendicular parallel or neither? Line aLine b Problem 2(3,1)(6,2)(5, 3)(11,5) Problem 3(5,-2)(6,6)(4,-5)(5,1) Problem 4(0,0)(3,4)(1,1) ( 5,-4) Problem 5(20,16)(8,4)(2,2)(-3,3)

17. Perpendicular lines that are vertical and horizontal Are the following pairs of lines perpendicar? What is the equation for both lines? What general rule can we come up wit hfor this situation?

18. Find a line that goes through a given point and is parallel to a given line. Find a line that goes through the point (1,6) and is parallel to y=2x+1 1. Slope of the line is 2 2. Fill in numbers for m,x and y y=mx+b 6 = 2(1)+b 3. Solve for b. b=4 4 Write your new equation with m and b y= 2x+4

19. Find a line that goes through a given point and is perpendicular to a given line. Find a line that goes through the point (1,6) and is perpendicular to y=2x+1 1. Slope of the line is -1/2 2. Fill in numbers for m,x and y y=mx+b 6 = -1/2(1)+b 3. Solve for b. b=6.5 4 Write your new equation with m and b y= -1/2x+6.5

20. Quiz 1. Find slope A. (2,6) (4, -4) B. (-4,5) (7, -3) 2. Are the lines a translation (2,5) (5,12) (-4,3) (-1,10) 3. Determine if the lines are parallel perpendicular or neither Y=2x+3, y= -1/2x -4 Y=-2/6x +1 y= -1/3x +4 Y = 5x y = 1/5x

21. When would it be important to find the distance from a point to a line? When you are riding a thirsty horse in the desert and you need to get to a river.

22. When would it be important to find the distance from a point to a line? When you are putting a sprinkler line together and you need to know the distance from the line to the sprinkler hook up

23. When would it be important to find the distance from a point to a line? When you are trying to figure out the altitude of a triangle on a coordinate plane. Altitude can help you find the area of a triangle.

24. Find the distance from a point to a line 1. graph the point and the line 2. Determine the equation of a line perpendicular to the line running through the point. 3. Use substitution to determine the intersection of 2 lines. Use distance formula to measure the distance from the point to the line. Y=2x+3 (2,2) 2=-1/2(2)+b 2= -1+b 3 = b Y=-1/2x+3 2x+3= -1/2x+3 x=0 y=3 Find distance from (0,3) to (2,2) = sqrt 5