• 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