PardekooperPardekooper

The graph of which function is shown ?

a. Y = 30xb. Y = 30 - xc. Y = 30 - (x+5)

d. y = 30 - 5x

0 2 4 6

0

10

20

30y

x

PardekooperPardekooper

0 2 4 6

0

10

20

30y

x

The graph of which function is shown ?

a. Y = 30xb. Y = 30 - xc. Y = 30 - (x+5)

d. y = 30 - 5x

Pardekooper

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What you’ll learnTo determine if two lines

are parallel or perpendicular by their

slopes, and To write equations of lines that pass through a given

point, parallel or perpendicular to the graph

of the given equation

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Two lines are Two lines are parallelparallel if if and only if they have the and only if they have the same slope.same slope.example:

example:

€

y = 4x + 5

€

y = 4x + 8

€

y =2

3x −5

€

y =−3

2x + 2

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Two lines are Two lines are perpendicularperpendicular if and only if their slopes if and only if their slopes are opposite inverses.are opposite inverses.

Here are some terms.

Is the following Is the following set of lines set of lines parallel or parallel or

perpendicular?perpendicular?y=2x+3y=2x-5

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parallel

Lets try some.

Is the following Is the following set of lines set of lines parallel or parallel or

perpendicular?perpendicular?

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Lets try some.

y=1/2x+3y= -2x-5

perpendicular

Is the following Is the following set of lines set of lines parallel or parallel or

perpendicular?perpendicular?

PardekooperPardekooper

Lets try some.

y=1/4x+1y=4x-1

neither

Write the equation Write the equation for the that is for the that is

parallel to y=5x-1 parallel to y=5x-1 with y-intercept of with y-intercept of

2.2.

m=5

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b=2

y=mx+by=5x+2

Where do the equations come

from?

Write the equation Write the equation for the that is for the that is

parallel to y=parallel to y=22//33x-1 x-1 with y-intercept of with y-intercept of

-1.-1.m=2/3

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b=-1

y=mx+by=2/3x-1

Where do the equations come

from?

m=-3/2

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b=-4

y=mx+by=-3/2x-4

Where do the equations come

from?Write the equation Write the equation for the that is for the that is perpendicular to perpendicular to y=y=22//33x-1 with y-x-1 with y-intercept of -4.intercept of -4.

m=4/1

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b=5

y=mx+by=4x+5

Where do the equations come

from?Write the equation for Write the equation for the that is the that is

perpendicular to y=perpendicular to y=--

11//44x-1 with y-x-1 with y-intercept of 5.intercept of 5.

m=2

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P(1,3)

y-y1=m(x-x1)y-3=2(x-1)

Where do the equations come

from?Write an equation for a line that passes through the point

(1,3)and is parallel to y=2x+4.

m=2/3

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P(2,-4)

y-y1=m(x-x1)y-(-4)=2/3(x-2)

Where do the equations come

from?Write an equation for a line that passes

through the point (2,-4)and is parallel to

y=2/3x+4.

m=-3/2

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P(1,-3)

y-y1=m(x-x1)y-(-3)=-

3/2(x-1)

Where do the equations come

from?Write an equation for a line that passes

through the point (1,-3)and is perpendicular

to y=2/3x+1.

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Why do we need to know if lines are parallel or

perpendicular ?Given a pair of Given a pair of opposite sides of a opposite sides of a quadrilateral are quadrilateral are

parallel, what does parallel, what does the quadrilateral the quadrilateral

look like ?look like ?

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Why do we need to know if lines are parallel or

perpendicular ?Given a pair of Given a pair of opposite sides of a opposite sides of a quadrilateral are quadrilateral are

parallel, what does parallel, what does the quadrilateral the quadrilateral

look like ?look like ?In order to know which one, you need more

information.

Given a pair of Given a pair of opposite sides of a opposite sides of a quadrilateral are quadrilateral are parallel and parallel and equal equal in lengthin length,what does ,what does the quadrilateral the quadrilateral

look like ?look like ?

Given a pair of Given a pair of opposite sides of a opposite sides of a quadrilateral are quadrilateral are parallel and parallel and equal equal in lengthin length,what does ,what does the quadrilateral the quadrilateral

look like ?look like ?

PardekooperPardekooper

Why do we need to know if lines are parallel or

perpendicular ?

We need some more information.

Given a pair of Given a pair of opposite sides of a opposite sides of a quadrilateral are quadrilateral are parallel and parallel and equal equal in lengthin length, and a , and a pair of adjacent pair of adjacent

sides form a right sides form a right angleangle,what does the ,what does the quadrilateral look quadrilateral look

like ?like ?

Geometry

Are the lines parallel, perpendicular or neither1. y = -5x 2. y=3x+1 3. y=1/2x-4 y = 5x - 18 y=-1/3x+4 y=1/2x+4

Write an equation for a line that passes through the point and is parallel to the given equation.4. (2,-7), y = x - 2 5. (1,-2), y = -2x + 7 6. (2,-1), y = -0.5x + 2

Write an equation for a line that passes through the point and is perpendicular to the given equation.7. (6,-2), y = 3/5x - 4 8. (3,7), y = 3/4x -1

9. Write an equation of the line that has an y-intercept of 3 and is perpendicular to the graph of 5x - 3y = 2.

10. Use slope to show that opposite sides of hexagon RSTUVW are parallel.

11. Use slope to determine whether a triangle with vertices G(3,2), H(8,5), and K(0,10) is a right triangle.

3.7 Slopes of Parallel and Perpendicular Lines3.7 Slopes of Parallel and Perpendicular Lines

W

R S

T

UV