Upload
nickolas-rice
View
222
Download
0
Embed Size (px)
DESCRIPTION
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
Citation preview
• Why did the girl wear glasses during math class?
Why was six afraid of seven?
What is slope? When is it used? How can it be found?
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• 5/1• 1/5• 2• -3
Slope fomula (y1 - y)/(x1- 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
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
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
When would it be important to determine if two lines are parallel
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?
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?
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?
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.
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.
Perpendicular lines
• Which of the following lines are perpendicular?
• Which of the following lines are parallel?
• Which of the following lines are neither?
Line a Line b
Problem 1 Y=2x+4 Y=-2x+3
Problem 2 Y= -3x+1 Y= -1/3x +2
Problem 3 Y= 5x +3 Y= -1/5x +1
Problem 4 Y= 3/4x+2 Y=3/4x -2
Problem 5 Y= -2/3x +1 Y=3/2x -1
Problem 6 2x+y = 8 X- 2y =12
Perpendicular lines
Are the two lines represented by the following points going to be perpendicular parallel or neither?
Line a Line b
Example
M=
(2,5)(-2,7) (3,6)(4,8)
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)
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?
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 yy=mx+b 6 = 2(1)+b• 3. Solve for b. b=4• 4 Write your new equation
with m and b• y= 2x+4
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
yy=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
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
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.
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
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.
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